Borini facing Southampton before he suffered the injury.
The Italian was replaced midway through the second-half of Saturday's 1-1 draw at Southampton after tearing a ligament in his groin.
Sunderland manager David Moyes admits that he was frustrated in his attempts to sign a new striker during the summer transfer window.
When it rains, it pours for David Moyes and his Sunderland side as a tough week only gets tougher due to the injury of Fabio Borini.
"It's an adductor muscle injury, and it's come off the bone".
Borini is one of Sunderland's only attacking options.
It leaves the club with Jermain Defoe, 33, as the only recognised striker alongside 17-year-old Swede Joel Asoro.
Sunderland's other forward options are 22-year-old winger Duncan Watmore and Manchester United's on-loan winger Adnan Januzaj, after Jeremain Lens was loaned to Fenerbahce.
Borini joins long-term absentees Vito Mannone and Sebastian Larsson in the treatment room, while Lee Cattermole and Jan Kirchhoff have not managed a single appearance between them so far this season. Norwich's Steven Naismith was heavily linked with a move to Wearside but it never came to fruition.
Sunderland are also looking to try and bring in some free agents in the coming weeks.
Moyes made eight new signings during the transfer window to bolster the squad he inherited from Sam Allardyce, but no strikers.