Long came on during the second half at St Mary???s but lasted less than 20 minutes before he was helped off following a collision with Palace defender Joel Ward.
The Republic of Ireland striker, whose stunning goal knocked out Ipswich in the previous round, was taken to hospital and is likely to join a lengthy injury list which includes Morgan Schneiderlin, Toby Alderweireld and Victor Wanyama.
“I spoke to the doctor and he thought he will have fractured one or two ribs and that’s very painful,” said Saints manager Ronald Koeman.
“It’s a pity because we don’t have that number of players to go with all the injuries that we have.
“I don’t know (how long he is out). Normally three, four, five weeks.”