The former Blackpool frontman picked up the injury last week and will have to undergo surgery in order to repair the fracture.
"We have found a stress fracture in the fifth metatarsal of his left foot," QPR's head physio Nigel Cox told the club's official website.
"He will have surgery on Thursday and will then be placed in an aircast boot for three weeks, which will immobilise the foot. Once he is out of the boot, and provided he is pain-free, we will push on the rehabilitation from there.
"For an injury of this nature you are looking at a timescale of six to eight weeks before the player can resume full training."
The striker will miss the newly-promoted side's Premier League clash with Chelsea this weekend.