The Brazilian midfielder was widely criticised following his £50million move to Old Trafford in the summer of 2018.
But while he floundered under Jose Mourinho, he has flourished under Solskjaer, and Schmeichel believes his former teammate deserves credit for his turnaround.
“Fred has been, for me, absolutely instrumental in how well the club has done this season,” Schmeichel said on Instagram Live with CNN.
“He was always perfect for the club but he’s now been given playing time and the more time he’s been given, the more confidence he’s gained and for me, he’s been one of the great stories this season at Manchester United.
“Of course it’s down to Fred but it’s down to Ole for giving him that confidence. I like that.”
As well as Fred, other stars such as Luke Shaw have shown improved form.
“I like the way he’s kind of introduced players that were already there but are now in the first team and are now playing well,” Schmeichel continued.
United went 11 games unbeaten prior to the season being suspended, and are now just three points off a top four spot, with Solskjaer also receiving plaudits for his off-field influence.
“He’s also brought all these values in. The players now know them,” the Danish former goalkeeper added.
“If you don’t share our values, there’s no place for you here. So you have to live up to his values.
“He’s bringing in his own culture and you can see it and it’s there and it’s brilliant.”