Solskjaer is furious Greenwood was called up by England just 20 days after finishing a year-long campaign with United during which he played 49 games and also questioned why the 18-year-old was put up for a news conference while on international duty.
Greenwood made his England debut against Iceland but was sent home in disgrace after breaking coronavirus protocols by meeting two women in the team hotel after the match.
"The kid had a fantastic season, he's just come through. I've worked and the club has worked and all the staff here have worked really hard too -- when we gave Mason enough time on the pitch, when we gave him 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 to the national team," Solskjaer told a news conference on Friday.
"I have to be honest enough to say I tried my best to give him a rest over the summer, at the club we asked specifically and pointed out he should have had a rest.
"He needs it mentally and physically after that season he had and the first thing that happens is one, he's called up and two, he's right there in the press.
"He needed a rest. I look at the interview and he's talking about looking at this season when it's over and it's the first day of the new season. He's an 18-year-old kid who needs managing."
Greenwood's indiscretions with England have complicated Solskjaer's summer, along with captain Harry Maguire's arrest while on holiday in Greece and a lack of progress with top transfer target Jadon Sancho.
United are still hoping to clinch Sancho's signature before the Oct. 5 deadline but time is running out.
"I can't say anything about other clubs' players, I can't speculate," Solskjaer said.
"We understand to get further we need to develop what we have and strengthen the team but let's wait and see if we manage to bring anyone in.
"I've been in dialogue with the club, we're always discussing and let's see if we can bring anyone in."
United kick off their season against Crystal Palace at Old Trafford on Saturday.
"I'm not going to tell you the team but the training, the goalkeeper training has been fantastic to watch," Solskjaer added.
"It's the highest possible quality you can imagine, I know the coaches are enjoying working with them and the stuff they do. Some of the stuff is fantastic and it's going to be interesting -- an interesting thing for many to follow."