The Scotland international has continued to play whilst struggling with the issue, but was forced to miss Saturday's 3-0 win over rivals Newcastle United.
Poyet now faces a decision over whether to send the 26-year-old for surgery, or continue to try and manage the problem throughout the remainder of the season as Sunderland fight to retain their Premier League status.
"It's affecting him more than I thought," he told The Sunderland Echo.
"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.
"We'll have to look at the games ahead and the chance of rest in between, but we'll beed to make a strong decision."
Poyet paired Fabio Borini and Jozy Altidore in attack in the win at Newcastle, while he can also call upon January signing Ignacio Scocco and England under-21 international Connor Wickham, who scoed eight goals in 11 appearances while on loan in the Championship with Sheffield Wednesday.
