The youngster fell over when he was challenged by Crystal Palace winger Wilfried Zaha in the 68th minute and was then caught on the knee by Yohan Cabaye.
He received medical treatment at Wembley before limping off the pitch, with Ashley Young replacing him as United secured the 2-1 victory in extra-time.
Rashford was the surprise inclusion in Hodgson’s provisional squad for Euro 2016 earlier this week following a spectacular debut season at Old Trafford.
It was feared his injury would rule him out of the upcoming friendlies, but reports suggest he will be assessed by England’s medical staff on Monday and is expected to train with the rest of the squad on Wednesday.
Rashford was unknown before his debut against FC Midtjylland in February and less than three months later he’s earned his first England call up, he could follow after Wayne Rooney, who scored four goals for England at Euro 2004 at the age of 18 and was named in UEFA’s team of the tournament and is now England’s top scorer.