"We have spoken with Modena police and even if this is an unpleasant event, it seems we can rule out an attack," said a spokesman, Michele Calderone, on Thursday.
"The author of the gesture was an unemployed man, with psychological troubles and we are working on the thesis of suicide," he added.
The man, who was apparently a Jordanian, set himself on fire. When police approached to try and put out the flames, the car, which ran on flammable liquid propane gas, exploded, the Ansa and Agi agencies reported, citing police.
No other injuries were reported.
"The man had shown uneasiness and problems relating to people in the past," a policeman in Modena told Reuters. "We think we're dealing with a suicide."
Police said the car was parked on a small, side street near one of the container walls that runs around the synagogue, about 50 to 80m from the main entrance.
Italy has stepped up security in recent weeks after a suicide bomber killed 19 Italians in southern Iraq last month. Italy has sent troops to Iraq to help US-led occupation forces there following the war to oust former president Saddam Hussein.
Security alerts were also raised around Europe following four suicide bomb attacks in Turkey in November, two of which hit synagogues. Sixty one people were killed in those attacks, claimed by groups linked to al-Qaida.