The injury to the 30-year-old will leave Tottenham without a recognized striker with Emmanuel Adebayor currently representing Togo in the Africa Cup of Nations.
The 30-year-old appeared to turn his left ankle as he avoided a challenge from Baggies striker Shane Long.
The striker was replaced by January signing Lewis Holtby before being helped down the tunnel by two members of Spurs' medical staff.
The injury means that Defoe is unlikely to feature during England's international friendly against Brazil on Wednesday night.
Tottenham manager Andre Villas-Boas is also likely to have his concerns after seeing his side's only available recognized forward limp down the tunnel.
Defoe's fellow strike partner Emmanuel Adebayor is also currently out of action for the Premier League side as he represents Togo in the Africa Cup of Nations.
However, the former Arsenal striker could return from international duty early, depending on Togo's result against Burkina Faso in Sunday evening's quarterfinal.