The Iranian international walked off the DW Stadium pitch clutching his hamstring and subsequently missed Saturday's 2-0 FA Cup defeat to Fulham at the MKM Stadium, which saw City produce a battling display against the Premier League outfit.
City coach Liam Rosenior admits the news is a blow to both City and the 21-year-old but says the initial prognosis suggested he could be out for longer than what's actually expected, so things are not as bad as they first feared.
“Allahyar has had a setback. It's not the same injury but it's the same hamstring,” Rosenior told Hull Live.
“He could be out for a month to six weeks depending on how we work with him which is a real blow.
"At the same time, those things happen in football and we now need to make sure that we manage him and make sure that he stays fit.
“He was really down. To be honest with you, we felt like the injury could have been a lot worse,” he added.