Maguire was handed a suspended 21-month sentence last month, having been found guilty of assaulting a police officer, swearing, resisting arrest and bribery during an incident in Mykonos.
He has denied the offences and has launched an appeal. The appeal nullifies the verdict and means Maguire has no criminal record ahead of a full retrial.
He's going to be our captain. He’s handled it really well and, of course, I’ll be here to support him
“He’s handled it really well and, of course, I’ll be here to support him,” Solskjaer told the official United website.
“He is going to be our captain. We’ll just leave Harry and his people and the process to run.”
Maguire was withdrawn from the England squad for last week’s Nations League double-header against Iceland and Denmark.
Solskjaer said: “Of course, Harry, as you said, had a difficult summer. He didn’t have a long break.
“His break was different to others as we gave him a few more days and, after, he’s come back and looked fine.
“For me, he is a top, an absolute top human being and has always been a positive guy with the right values. So I really hope we can see Harry performing at his best.”
England manager Gareth Southgate plans to bring Maguire back into the England set-up next month for the friendly with Wales and the Nations League double-header with Belgium and Denmark.
Southgate initially included Maguire in his squad for the Iceland and Denmark matches but then withdrew him hours later following the conclusion of his court case in Syros.
Maguire went on holiday to Mykonos after United’s season ended with a Europa League semi-final defeat against Sevilla in Cologne.
Maguire, 27, became the world’s most expensive defender when joining United from Leicester for £80million in August 2019.
He was named as United’s club captain in January following Ashley Young’s departure to Inter Milan.
Maguire played in every minute of United’s 38 game Premier League campaign, becoming the first outfield player to do so for the club since 1995.