The 27-year-old striker has been an integral part of Martin Jol's plans so far this season but has suffered a recurrence of a strain that has blighted him already this campaign.
The news will come as a bitter blow to the 56-year-old Dutch boss, having seen the Costa Rican international restricted to just nine league appearances through injury so far already this term.
However, after aggravating his hamstring once again, he faces four more weeks confined to the treatment table, as the club seeks to end its recent run of poor form.
"It's a big disappointment because Bryan is a vital player for us," Jol told reporters.
Meanwhile, right back Sascha Riether remains a doubt for the club's home game against Newcastle on Monday evening, after he picked up a "minor knee strain" during the club's 3-0 defeat at Craven Cottage to Tottenham.