The English winger made his return to the starting line up against Atalanta in the Champions League, scoring to help United on their way to a 3-2 win after being 0-2 down at half time.
However, Rashford came off in the second-half of the game, prompting concerns about his fitness.
Asked about the matter, Solskjaer said: "I don't know. I hope so and I think so.
"It's a dead leg. Sometimes that can take longer than what you want but if we treat it well he should be okay.
"He's worked really hard. His injury was, or [because of] the surgery, he couldn't train with contact but he's been training physically and now he's physically robust. It's about getting his football form back in.
"Marcus is a natural talent but he wants to work on his game and he has worked without contact allowed and today he took us his goal really well."
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