Greenwood and Manchester City’s Phil Foden were sent home by Gareth Southgate after meeting up with two women after the Nations League game against Iceland earlier this month.
The England manager described their actions as “unacceptable” and both players have since made public apologies.
But Solskjaer claims Greenwood should never have been called up by the Three Lions after such an exhausting first season of senior football.
“The kid had a fantastic season, he’s just come through,” said the United manager. “I’ve worked and the club have worked really hard to decide when we gave Mason enough time on the pitch, exposure in the media.
“Then you come to the end of the season and we’ve had less than two weeks off and he’s called up. I tried my best to give him a rest over the summer. We asked specifically that he should have had a rest. He needs it mentally and physically and first thing that happens he’s called up and right there in the press.
“We’ve done what we can to protect him. I’ve done what I can to help him, when he comes back into the daily routine he’ll be fine.”
Solskjaer insist Greenwood is part of his plans for Saturday’s game against Crystal Palace.
He added: “I’ve spoken to Mason and what we speak about and discuss will be between the two of us.
“He’s a big part of this club. This is where he is at home. We challenge him – he’s got people looking after him.
“We had a plan and I think it worked really well, but he needed a rest.
“I looked at the interview with England and he’s talking about looking at this season when it’s over and it’s first day of new season. He’s an 18-year-old kid who needs managing.”