Gaza police say they are investigating the blast, which occurred yesterday night.
Officials at the center say no one was in the building at the time of the explosion and that most of the damage was in the facility's restaurant.
The French Cultural Center in Gaza conducts French language courses and transfers visa applications for France from local residents to the French Consulate in Jerusalem for processing.
Gaza was hit hard in a 50-day war this summer between Israel and Hamas. The deadly conflict also destroyed or damaged more than 60,000 homes and more than 5,000 businesses, according to joint assessments by the Palestinian government and the United Nations.