Maguire is enduring a difficult season with the Red Devils and was even booed while on international duty with England recently.
The 29-year-old was again at the wrong end of things at the weekend when Anthony Gordon's strike deflected off him for the only goal in Everton's 1-0 win over Manchester United.
The defeat left Rangnick's side seventh on the table, six points behind Tottenham Hotspurs in fourth place.
Vidic, who starred for Manchester United between 2006 and 2014, reckons Old Trafford's current captain is going through a tough period and should be taken out of the firing line for some time.
"Every player has a problem with form at some time in his career," Vidic, who played for United between 2006 and 2014, told The Athletic. "I did and it's clear that Maguire is not at his best this season.
"I think you can do a few things and one of them is not to play every match as you try to find form again and get confidence.
"A coach could play him in easier games, not that there are many in the Premier League, and take him out for harder matches. The player needs to feel powerful and strong on the pitch again, not as it is now where he feels that it's not happening for him.
"It's difficult to play well when you're under so much pressure because people are waiting for you to make a mistake. You're asking me this and I'm replying as a coach."
"It's not a problem if a player says to his coach that he's not feeling great on the pitch," he added.
"If he says: 'Give me a break, give me a couple of weeks to regroup and train well and then play again'. I had some horrible games for United and needed to find my peace and grow again.”
