Martial's stunning goal in Saturday's 3-0 demolition of Fulham was his 11th of the season.
Solskjaer said afterwards: “I am glad he is in my team. He has contributed to so many chances, so many goals. He is a Manchester United player. He excites the crowd. He excites the manager. He excites his team-mates. And he is a great character around the place.
“He does have similarities [to Cristiano Ronaldo], of course. If he wants to be a Cristiano's level, Anthony knows what he has to do. It is up to him. He has the talent."
Solskjaer insisted he has struck the balance between Martial racking up the goals and tracking back to help his defence.
The former United striker added: “He knows he needs to do some defensive work but he has got some quality going forward.
“He is electric and his balance, his pace, everything about him is, well, when you are a full-back, you don't want him running at you. He knows he has to defend."