Martial suffered a knee injury while away with France last week.
Solskjaer said this morning: "Anthony has started his recovery. If we see him before end of season I'll be very surprised.
“But, of course, he is determined to come back as quickly as he can. There are important games for us before the end of the season and then there are the Euros [with France, in the summer].
“He has already come in [to the training ground], he is bright around the place. [He's] disappointed he can't help us now, but, of course, he wants to work to get back as quickly as possible."