The teenage striker scored his 16th goal of the season in United's 3-0 win against Aston Villa and Solskjaer feels that Greenwood has become irreplaceable.
The Norwegian coach said: "It's up to him [Greenwood] how far he wants to go.
"I am doing my bit to help him but he has to do it - turn in performances in training, in games, live his life properly. It's up to him how far he wants to go.
"He's 18 and of course he will get better. He is a natural footballer and has been in the academy since he was a little boy. His dad showed me a picture of us together when he was seven. He knows we believe in him. You cannot leave players out when they score goals."
United have now won four league games in a row to move within a point of the Champions League places and midfielder Paul Pogba suggests the team are putting in performances worthy of the club's famous name.
The French World Cup winner said: "We are really pleased with ourselves because we know we have to carry on. We talk before the game, in training, Manchester is a big club and we want to keep the level up always.
"The performances of the past few weeks are Manchester United. We have to keep working, there is a lot to do."