The Ivorian picked up an injury in Sunday's 1-1 draw with Newcastle.
It was initially feared Zaha would miss the rest of the season.
Such a blow would have been catastrophic for the Eagles.
Zaha has been arguably their most important player this season, having played an integral role in lifting them out of the relegation zone.
Palace have not won a Premier League match without the 25-year-old since September 2016.