It comes after Councillor Nutting came under fire for comments when discussing Shrewsbury's Clive of India statue, though Shropshire Council insists the training is a refresher he would have been due to take anyway.
Councillor Nutting was criticised for saying "all lives matter" in a discussion relating to the statue, and that you shouldn't pick one section of society over another.
He said he wanted the monument to remain.
It comes after much debate over whether historic statues should be torn down and following an outpouring of support for Black Lives Matter.
To say "all lives matter" in relation to the anti-racism movement is considered by many as an attempt to diminish the message.
Councillor Nutting is now scheduled to undertake diversity training.
Karen Bradshaw, Shropshire Council’s acting interim chief executive, said: “In his interview Councillor Nutting made clear that retaining the Clive of India statue is very much his personal view.
"A final decision is likely to be taken at a future meeting of the full council. At no point did he say that the council would not consult with members of the BAME community.
"We want to make clear that of course Shropshire Council would want to hear from, and talk to, members of the BAME and Asian community on any issues that are of interest or concern to then, including the future of the Clive statute.
“All Shropshire councillors are invited to attend equality and diversity training when they are first elected to the council, and then refreshed on a regular basis.
"Councillor Nutting has attended this training but, as it was some time ago, he has confirmed that he is scheduled to, and will, undertake refresher diversity training.”
Sundorne councillor Kev Pardy described Councillor Nutting's words as "naive".
Councillor Pardy added that he hasn't been on a diversity training session with the council since 2013 and doesn't remember being invited to one since.
He said Labour colleagues also don't remember being invited recently and that two new councillors within the party have not had the training.
He said: "When I joined the council they had courses and I went on one, which was really good.I haven't been offered a refresher since.
"It was really interesting and helped us understand how other people lived their lives and how they fit into society. It was quite enlightening and I think they are important to attend and there should be regular refreshers."
Shropshire Council has been approached for a comment about it's diversity training policy for councillors and when the last sessions were held.