Greenwood, 19, overtook Wayne Rooney as United's top-scoring teenager in Premier League history in Sunday's 3-1 win over Aston Villa.
That match followed Thursday's second leg of the Europa League semi-final at Roma and comes ahead of games this week against Leicester and Liverpool, both of whom have aspirations to finish in the top four.
Victory for United in both matches would cut Manchester City's lead at the top of the table to just four points but realistically would only delay the Etihad title party.
Solskjaer substituted Greenwood with 25 minutes remaining of the Villa game to keep the England forward as fresh as possible.
"Yeah, he's tired, his body is not really filled out yet and he might not be ready for all of these games but he's got something special," said the United boss, whose side are now guaranteed a place in next season's Champions League.