Martial limped out of France’s World Cup qualifier against Kazakhstan last weekend, making him a doubt for Sunday’s Premier League clash with Brighton.
The 25-year-old missed out on the squad to face Brighton, and Solskjaer now expects to be without the United forward for a key period.
“Unfortunately he’s sprained his knee with France,” the United boss told MUTV.
“It’s always when they go away on internationals, you’ve fingers crossed and you hope that they’re going to come back fit.
“Paul (Pogba) played in all three games – 30, 60, 90 minutes – so that was a boost for us but losing Anthony for what might be the rest of the season is very disappointing, especially when the reports and signals are from there that it wasn’t serious but it looks a bad one, yeah.”
Additional reporting by PA.