Sean Bean won best actor, and the production, which also stars Stephen Graham, won best mini-series at the glittering ceremony at London's Royal Festival Hall.
The BBC One drama stars Bean as Mark Cobden, a new prisoner consumed by guilt for his crime, and way out of his depth in the volatile world of prison life. He meets Eric McNally (Graham), an excellent prison officer doing his best to protect those in his charge. However, when one of the most dangerous inmates identifies his weakness, Eric faces an impossible choice between his principles and his family.
The three-part mini-series was filmed on location at the prison for nine weeks in October 2020, and was first screened in June last year.
Prison owner Joel Campbell was thrilled that Time emerged victorious.
He said: "It's great for the production. I'm pretty sure that those are the highest awards for a production associated with the prison.
"It's fantastic that Sean Bean won best actor, and it won best mini-series as well up against big competition.
"I think as well at the production, it's also down to the location. If it wasn't for Shrewsbury Prison as the backdrop, it wouldn't have felt like a prison drama. It's just as much a part of it."
He added: "We brought a number of things to the production. For example, one of our ex-prison officers Graham Goodwin spent a couple of hours with Stephen Graham about how prison officers work and their mannerisms. When I seeing him in the production doing certain things, like how he stands and holds the door, I can tell that's how a prison officer would act and hold themselves."
Now the prison is preparing to set up Stephen Graham's office and Sean Bean's cell as they were in the show. Several items of memorabilia have been gathered so visitors to the prison can learn the story of their time at the location.
"We've put all the same kit in there, and we're just in the process of setting up," said Joel. "We've got all sorts of stuff to go in there, including a tissue from when Sean Bean got punched on the nose - obviously with fake blood."
He added: "It was a bit difficult for us to meet the actors on this production because it was filmed at the height of Covid in October 2020. A lot of industries were locked down, but they did allow filming. The actors were kept in a very tight bubble over the nine weeks.
"I did get to meet Stephen Graham for about 10 minutes or so. Our prison officer spent more time with him, and said he was just an incredibly professional actor. He wanted to absorb all the knowledge and get himself really into this role.
"There were about 150 to 170 people here every day. It was a big production. It's testament to them that they were able to run such a big production during Covid and for it to be received so well.
"It was great to have Shrewsbury Prison used in the way it was. Now it has been commissioned for a season two. Hopefully they will come back to Shrewsbury, but time will tell."