The club captain has played with the injury in recent games but a precautionary X-ray at the start of the week has revealed the true extent of the problem.
"We think Robert will be out for four or five weeks because he's fractured his right foot," manager Steve Bruce told the Premier league club's official website.
"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 played in all four of the club's Premier League games so far but Bruce insists his absence opens the door for someone else to stake a claim.
"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."