The 26-year-old has been dealing with an Achilles problem, which put him out of Saturday's 3-0 win over Newcastle United, for a number of weeks.
"It's affecting him more than I thought," Poyet told the Shields Gazette. "I'm a bit worried about it. We're analysing it with the medical staff, but we're going to have to make a decision one way or the other."
Fletcher is believed to have seen a specialist earlier this week.