Maguire was given a suspended 21-month sentence last month after the England defender was found guilty of assaulting a police officer, swearing, resisting arrest and bribery during an incident in Mykonos.
The 27-year-old has denied the offences and has launched an appeal which nullifies the verdict and means he has no criminal record ahead of a full retrial.
Following the original court verdict, Maguire was withdrawn from England’s squad for their recent Nations League matches against Iceland and Denmark.
However, England manager Gareth Southgate has said would consider bringing Maguire back into the squad for the next internationals.
Now United boss Solskjaer has made it clear he will not punish his centre-back by stripping him of the captaincy.
“He’s handled it really well and, of course, I’ll be here to support him,” Solskjaer told United’s website on Saturday.
“He is going to be our captain. We’ll just leave Harry and his people and the process to run.”
Maguire was a key figure in his first season with United following his £80 million ($102 million) move from Leicester, which made him the world’s most expensive defender.
Solskjaer said Maguire had coped well with the incident in Greece, which was allegedly sparked when the player and his family and friends were taunted and attacked at a nightclub.
“Of course, Harry, as you said, had a difficult summer. He didn’t have a long break,” Solskjaer said.
“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.”
United start their Premier League campaign against Crystal Palace on September 19 after being given an extra week of rest following their involvement in the Europa League in August.