The Republic of Ireland international sustained the injury after being introduced as a second-half substitute during last weekend's 3-2 FA Cup fourth-round defeat to Crystal Palace.
Long netted the winner against Ipswich Town in the previous round - his fourth goal in Southampton colours since his move from Hull City in August.
"Shane is out for three to four weeks more because he has fractured one of his ribs and it’s very painful, that’s a shame," manager Ronald Koeman confirmed at a press conference ahead of Sunday's Premier League clash with Swansea City.
Long's absence and Jack Cork's expected switch to Swansea means Koeman is keen to be active in the transfer market before Monday's deadline and he has Tonny Vilhena and Filip Djuricic in his sights.
Vilhena is a holding midfielder and would be a direct replacement for Cork. The 20-year-old played under Koeman at Feyenoord, where his former boss suggested he is unsettled.
Djuricic, a 23-year-old attacking midfielder and Serbia international, is presently on loan at Bundesliga outfit Mainz from Benfica.
"There’s a good chance that one of the two players, and maybe both players [join Southampton]," Koeman said.
"We are interested in [Vilhena] because that player is not happy in Feyenoord. He likes to play more and is interested in changing the club.
"I like the player, I believe in the qualities of the player, he's a young player who is 20 years old.
"It's one of the philosophies of the club to have young players and if I can help the player I like to do it."
On Djuricic, he added: "I am interested in the player, it's a good young player who can play in different positions but I don't have any update at this moment."
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