Police spokesman Ayman Betjeni said "this was a cowardly attack and unfortunately the second incident of this sort in... two months.
"It seems as if there are elements who want to disturb Gaza's security and are targeting foreigners to intimidate them and give a bad image of Gaza."
He said all streets leading from the scene had been closed off and that "investigators were on the scene trying to identify the perpetrators".
"The explosion was just behind the building and damaged a wall," the photographer said.
A source connected with the centre said one or two explosions had damaged the south wall of the compound as well as some of the facade of the building, which also houses the local branch of the French consulate.
On October 8, the centre's offices were set ablaze after the apparent explosion of two faulty fuel tanks.
Signup to our newsletter and follow us on Facebook and Twitter!
The centre had been closed at the time for the Muslim Eid al-Adha holiday.
Police at the time suggested the explosion may have been a criminal act, but the results of their investigation were never released.
French diplomatic missions and official buildings have been on high alert since the start of a spate of kidnappings and beheadings of foreigners by Islamic State jihadists and their allies, particularly that of Frenchman Herve Gourdel in Algeria.
France has angered IS by taking part in air strikes on the group's forces in Iraq.
Friday's blasts came a day after a suicide bomber struck at a high school attached to the French cultural centre in Kabul, killing at least one person and wounding 15.
The Gaza Strip, subject to an Israeli blockade and battered by a July-August Israeli military offensive, suffers chronic power cuts, leading to the widespread use of privately owned generators and storage of jerrycans of diesel fuel to power them.