The Slovenia international sustained the injury earlier in the season, but has played through the pain barrier as Hull made their return to the Premier League.
Bruce has revealed the 32-year-old has sustained further damage as a result of playing on and will be unavailable for at least a month.
Koren has started all four of Hull's league fixtures this season and Bruce said: "We think Robert will be out for four or five weeks because he’s fractured his right foot.
"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.
"So we scanned it and x-rayed it and those have revealed a hairline fracture to one of the bones in his foot."
Koren made 40 league appearances as Hull secured promotion from the Championship last season.