The 32-year-old missed the 2-2 draw with Burnley on Saturday and has a fight on his hands to return before the March international break.
The injury is a blow for Marco Silva as he loses his improving joint-top scorer with five goals this season.
Fulham are assessing Jimenez week-by-week as they set out a timeframe for his return and the worst case scenario would see him miss six league matches, including Bournemouth's visit to Craven Cottage on Saturday.
Silva explained before the recent trip to Burnley: "It is not something that is going to be quick [to recover from]".
Rodrigo Muniz scored his first Premier League goal as he started in place of the Mexican at Turf Moor.
Meanwhile, Chelsea striker Armando Broja made his debut for the Cottagers from the bench after joining the club on loan until the end of the season.
Broja is not seen as a replacement for Jimenez but is well-placed to become a regular starter in the coming weeks.
Silva explained why Fulham spent January searching for a striker before Broja's loan deal was agreed in the final hours on deadline day.
"It's not just because Raul got injured, but in the summer, we sold a striker [Aleksandar Mitrovic] for a big amount of money," he added.
"It was important in the summer, and it is important now."