The midfielder has been carrying the injury for several weeks but has struggled with increasing pain and was sent for X-rays at the start of this week to assess the extent of the damage.
Koren will now miss this weekend's trip to Newcastle in the Barclays Premier League, in addition to subsequent matches with West Ham, Aston Villa and Everton.
"We think Robert will be out for four or five weeks because he's fractured his right foot," Hull manager Steve Bruce said on hullcityafc.net.
"That is a bitter blow to us. He did it a couple of weeks ago and to be fair he's played with it.
"But last Saturday it was worse and so we scanned it and X-rayed it and those have revealed a hairline fracture to one of the bones in his foot."
Koren has been an ever-present in midfield as the Tigers racked up a win, a draw and two defeats from their opening four matches on their return to the top flight.
And while disappointed to lose the services of the 32-year-old, Bruce admits his absence opens the door for the likes of George Boyd and Stephen Quinn to impress.
"When somebody is out injured, somebody else is going to get a chance - that is how football works," he said.
"There's a few that have been champing at the bit with the likes of George Boyd and Stephen Quinn in particular, so one of them will step into the breach."