The 28-year-old forward was forced off just 14 minutes after his introduction in the second half of Saturday's FA Cup fourth-round exit to Crystal Palace.
The collision with Palace defender Joel Ward during the 3-2 loss saw Long taken to hospital and Press Association Sport understands he now faces between four and six weeks out of action
The Republic of Ireland international fractured his ribs but did not sustain a punctured lung, contrary to reports, with his absence another big blow for Champions League-chasing Saints.
Toby Alderweireld, Victor Wanyama and Morgan Schneiderlin are all unavailable at the moment through injury, joining long-term absentees Sam Gallagher and Jay Rodriguez in the treatment room.
International commitments mean Sadio Mane, Emmanuel Mayuka and Maya Yoshida have reduced Ronald Koeman's options further.
Source : PA
Source: PA