The striker started Friday's 1-0 win over the Republic of Ireland in Glasgow on Friday, but was substituted with the injury after 56 minutes.
Fletcher confirmed he will definitely miss Scotland's clash with England on Tuesday, but has his fingers crossed the problem will not leave him on the sidelines for too long.
"I have no chance of making the England game," Fletcher told The Chronicle.
"I just hope I can be back for the Sunderland game at the weekend, but even then I need to wait and see what the extent of the injury is.
"I went to get a scan on Saturday so I am just waiting for the results."
The 27-year-old has suffered badly with injury in recent seasons with a broken foot and dislocated shoulder keeping him out of selection for months at a time.
Fletcher has struck four goals in his eight Premier League starts.
