The striker picked up the injury in Sunday's goalless draw at Swansea City, making way for Matt Jarvis in the 34th minute, but the Upton Park club refused to speculate on exactly how long the 27-year-old would be out of action.
However, the Portuguese star suffered a similar injury last October, and went on to miss almost three months of the season.
After being taken to hospital on Sunday evening, a club spokesman confirmed his condition would be assessed over the coming days.
The news will come as a blow to manager Sam Allardyce, who recently re-signed Carlton Cole as he looked to cope with a striker shortage.
Vaz Te has made nine appearances in all competitions for West Ham this season, scoring four goals.
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