Father-of-three Gareth Utting, a 37-year-old English teacher at Thomas Adams High School in Wem, died suddenly last month.
His wife Alison Utting has now written an open letter to Mr Gove to help spread awareness of the pressures teachers are being put under.
Speaking to the Shropshire Star Mrs Utting, 41, said today: "He was a fantastic person but he was killed by the system.
"What happened to Gareth should not have happened and we should not be in this situation.
"It's not straightforward and simple to say that it was teaching that killed him, but anyone who knows or lives with a teacher know the stress they are under."
She added: "When Gareth died in hospital one of our first questions was whether we could donate his organs because Gareth would have wanted that.
"Unfortunately we were told we couldn't because of the nature of Gareth's death and the CPR.
"While we are suffering this tragedy we also wanted to carry on that and try and help someone somewhere else, and this letter was a way of doing that.
"We wanted to do this to help so that no-one has to go through what we are going through."
In the letter Mrs Utting writes: "There were a few contributory factors to his (Gareth's) death, but looming large was the word 'stress'.
"I should be proud that my husband was a teacher. But right at this moment, I'm not. I'm sorry that he was. Because if he had a different job, he might still be with us.
She also says she wishes she had done more to help him get out of teaching.
Mrs Utting, who lived with her husband and their three children in Ellesmere, said teachers were struggling under pressures from above, which she says have greatly increased.
The letter says: "I don't see better education. I see good teachers breaking under the load. I see good teachers embittered and weary. I see good teachers leaving the profession. I see good teachers never even entering the profession, for fear of what lies ahead."
She also urges Mr Gove to rethink how education is run.
She says: "I don't know what I want to ask of you. All I know is that the situation as it stands is wrong. On behalf of all the teachers and pupils out there, I beg you to go back to the drawing board. Learn from your mistakes."
Mr Utting was taken ill while exercising at his home in Cherry Drive and died of a heart attack later that same day at Royal Shrewsbury Hospital.
A spokesman for the Department of Education said they did not feel it was appropriate to comment as Mrs Utting expressed in her letter her desire for Mr Gove not to send his condolences.
Wifes open letter to Michael Gove over the problems teachers face:
"Dear Mr Gove,
I am writing to inform you of the death of Mr Gareth Utting, a teacher of English at a secondary school in Shropshire.
Gareth died at the age of 37 of a massive heart attack. There were a few contributory factors to his death, but looming large was the word "stress".
He leaves me a widow with three children, aged fourteen, four and one.
This is not the angry rant of a bereaved person.
I haven't got anywhere near angry yet. I am still reeling with shock and wondering if there was anything I could have done to prevent my husband's death. When these thoughts beset me, I keep coming back to the fact that I should have done more to help him get out of teaching.
And how can that be right, to think that? I love teaching.
In the few weeks since Gareth died, I have heard and read so many tributes from his students that attest to the positive impact that a good teacher can make. I should be proud that my husband was a teacher. But right at this moment, I'm not. I'm sorry that he was. Because if he had a different job, he might still be with us.
I don't pretend to know the ins and outs of the changes that have hit teachers in the last few years. I qualified as a teacher myself but have been at home raising our young children, so have not been directly involved. But I can tell you what I see around me.
Teachers like Gareth have changed.
Their hopes for the young people in their care have not changed. Neither has their willingness to go the extra mile to help those young people to succeed. But the work-load that they struggle under and the pressures that are applied to them from above have greatly increased. If this led to better education for our children, then I would be supporting these changes.
But I don't see better education. I see good teachers breaking under the load.
I see good teachers embittered and weary.
I see good teachers leaving the profession.
I see good teachers never even entering the profession, for fear of what lies ahead.
I see pupils indoctrinated with achievement targets, who are afraid to veer from the curriculum in case it affects their next assessment; pupils for whom "knowledge" is defined by a pass mark and their position within a cohort. Within this atmosphere, my husband struggled to help his pupils in every way he could. The comments that they have left on social media reflect a teacher-pupil relationship that was honest, helpful and mutually respectful.
He taught them English, and they did well at it. But he also taught them about life, and love, and self-esteem. But he did this in spite of, not because of, the current state of the education system. Gareth is at peace now. But I have some difficult choices to make. Do I return to a profession that takes so high a toll? When my four-year-old son says he wants to be a teacher, do I smile or try to talk him out of it?
When I see Gareth's colleagues, do I congratulate them for being so amazing, or encourage them to explore other career options?
Mr Gove, I don't envy you your job. I don't know the best way to achieve a high standard of education for all pupils, everywhere. But I do know this: People don't become teachers to be slackers, for the pension or for the name badge. Here's an interesting theory of mine that I was discussing recently with my husband. If you took away all external inspection and supervision, all targets and reviews, if teachers were left to themselves to teach what they wanted to teach, the way they wanted to teach it, what do you think would happen?
This is what I think: Every teacher that I know cares deeply about their subject and their students. They would teach marvellously.
They would share knowledge and encourage each other. They would deal with problems (including less-than-perfect pupils and teachers) with the professionalism that they possess in spades. Of course we cannot remove all monitoring of teachers and schools. But it seems to me that you have forgotten this basic fact: Teachers love to teach, and they want to do it well.
I don't know what I want to ask of you. All I know is that the situation as it stands is wrong.
On behalf of all the teachers and pupils out there, I beg you to go back to the drawing-board.
Learn from your mistakes. Gain knowledge. And please don't send me your condolences.
Star comment: Strain for teachers revealed