The Samoan winger was carried off after 50 minutes during Chiefs 24-21 loss at Northampton Saints on Sunday with what looked like a serious ankle problem.
The 25-year-old missed the second half of last season through injury and Chiefs coach Rob Baxter has admitted that it doesn't look good for Tatupu at this early stage.
"It is looking relatively bad at this early stage, and we will know a little bit more when we have been able to assess it properly, but I am really hopeful it is not too bad," Exeter head coach Rob Baxter explained.
"The lad has been fantastic coming back from his last injury, and I am really hopeful we can get him back on the pitch as soon as possible."
Next up for Chiefs is a trip to London Welsh on Sunday.