Middlesbrough will be without Tuncay's services until the end of October after it was confirmed that the Turkey international suffered knee ligament damage while on international duty last week.
It had been feared that Tuncay would be sidelined for several months but Boro's medical department believe he should be ready for a first-team return within six weeks.
"It's a shame for Tuncay," boss Gareth Southgate told Boro's official website.
"However, we've got strength in depth in that area now and it gives opportunities to the other lads."
It is also hoped that Didier Digard's knee injury is not serious and the Frenchman could return to action shortly.
The 22-year-old suffered the injury midway through the second half at Portsmouth on Saturday.
However, it seems certain that Digard will miss Saturday's Premier League encounter with Sunderland, as will fellow central midfielders Julio Arca and Mohamed Shawky.