The officer's injuries are not believed to be life-threatening after the explosion occurred between 8am and 8.30am (7am to 7.30am BST) on Saturday.
According to authorities, five people, including a rabbi, were inside the synagogue at the time.
The explosion was caused by two vehicles burning outside.
A police source told French media that gas canisters were hidden in one of the vehicles.
The suspect, who was reportedly carrying a Palestinian flag, also set fire to several of the synagogue's entrance doors.
Jewish community leader Jonathan Arfi said the incident was “an attempt to kill Jews” and appeared to have been planned to target worshippers on Saturday morning.
President Emmanuel Macron called the incident an “act of terrorism.”
A witness, who asked not to be named, told the BBC: “As we rounded the last corner there was a huge explosion. There was a fireball flying into the air.
“It was surreal, like a movie. It didn't go any further.”
Prime Minister Gabriel Attal and Mr Darmanin visited the site on Saturday evening. Both have previously condemned the attack, with Mr Attal calling it an “anti-Semitic act”.
“What happened here shocked and outraged every Republican in our country,” Atat said during his visit.
“The reality is that French Jews are once again being targeted and attacked for their beliefs.”
Mr Atal said that if the synagogue had been full of worshippers “there would have been many more casualties” and that an “absolute tragedy” could have been “narrowly avoided”.
Both Mr. Atal and Mr. Darmanin said security outside the synagogue would be increased.
“I pledge my full support to my fellow Jewish citizens and to the local government,” Mr. Darmanin said this morning.
