Fletcher made his first appearance in nearly 12 months at the weekend as he came on for the final 20 minutes of Manchester United's 3-0 victory over Aston Villa.
He has been plagued by a chronic bowel condition since November 2011 and Strachan is delighted to see him back in action, admitting that he did not realise the 29-year-old was so close to a return.
Fletcher will give Strachan another valuable option in midfield, but the Scotland boss not want not to put him under any pressure by rushing a comeback to the international arena.
"We'll just see how it goes now for the next couple of months," Strachan told the Daily Record.
"We'll let him enjoy this and get in touch with him to tell him how happy we are for him.
"I tried to speak to him over the weekend and we just kept missing each other. But I didn't know he was so close to coming back to be honest.
"When I got a text saying he was going on as a substitute on Sunday it was amazing.
"For us he adds to what we have in the middle of the park which is absolutely fantastic.
"But we'll let him take his time. I think that's what he wants as well.
"He's a top player though. He moves people round about him. As he plays he organises and not every player can do that."
Strachan believes Fletcher can return to his best form and play a crucial role again for United, who have struggled so far this season.
He added: "Last week I was asked on TV about Manchester United and how they were doing and what they were missing.
"I think it could be him. People maybe took it for granted before his illness but any time United were in trouble he played. In all the big games he played.
"I actually see him as being a leftover from that class of 1992. I know he wasn't part of that group but he has that in him, where winning is the most important thing at the football club."