McTominay returned from a three-and-a-half week lay-off with an ankle injury to underpin United's first win in four against Jose Mourinho's Spurs at Old Trafford.
Solskjaer claimed on the eve of the Tottenham game no United players were 'undroppable' but has made an exception.
"You can almost say he (McTominay) is undroppable at the moment. I wasn't gonna try to push him through for this game. The physical presence he gives us, the leadership he gives us in midfield also releases Fred.
"I thought Fred was excellent today and maybe the one chance [Spurs] had he blocked. First class, they are a good partnership.
"He trained yesterday and that was just a light session with the reserves, but he's a tough boy. There's no chance he's gonna say 'no thanks' if he felt okay, so it's probably the first time I've really really pushed players that haven't had the foundation but he's so fit anyway."
The United manager continued: "The first big game he played for me was Liverpool last year.
"And he was absolutely top class, you didn't expect anything else, because see a boy doing everything right every single day in training, and he prepares properly and they're the boys you wanna have in the team.
"He's so professional, he's not tainted by any superstar or fame, he just wants to become the best footballer he can be and that's the people I want in this club.
"He would've suited my squad when I played, he would've fit right in that squad because he's come through the academy, he's one of ours, he's one of the locals and knows what Man United means."