The captain has not sat out a United match since the FA Cup fifth round win at Derby County on March 5 and he started 61 games for club and country last season.
"No," Solskjaer replied when asked if Maguire required a breather. "He just needs to play to get sharper and fitter and he never wants to rest, he wants to play every game."
With United only 1-0 up at Luton, Solskjaer introduced Bruno Fernandes, Marcus Rashford and Mason Greenwood in the 78th minute nd Fernandes played Rashford through to score before Greenwood opened his account for the season.
The trio are expected to start in Saturday's lunchtime trip to Brighton and Solskjaer was reluctant to give him too much playing time against Luton.
"It wasn't planned for them to play, I don't plan ahead that much," Solskjaer explained. "You just see wherever you have to make changes. They've got a decent (training) session tomorrow, so I don't want them to play too much.
"They did well when they came on, got the runs and work in. When you're 1-0 up you don't wanna weaken your team when you make subs."