The pair were leaving the club, called Casablanca, in Nouakchott at about 2am (0200 GMT).
Three shots hit their car, while four other shots were aimed at the club's gates, injuring the two Mauritanians who were entering at the time, Sayid reported.
Mohamed Lemine Ould-Zeine, the governor of Nouakchott, said that those injured had been admitted to hospital and were not in a serious condition.
It is unclear if the gang was a criminal one or was acting for political reasons.
Hamza Ould Bilal, a taxi driver at the scene, said the men had driven up to the area in a car and grouped by a discotheque next to the embassy. Bilal said the men then opened fire before being repelled by the guards.
Mauritanian soldiers have since cordoned off the neighbourhood.
Embassy staff safe
Boaz Bismuth, the Israeli ambassador to Mauritania, said that no embassy staff were hurt.
"At 2:20 this morning, there was shooting at the Israeli embassy in Nouakchott. All the embassy staff, Israeli and Mauritanian, are safe."
Political parties in Mauritania have recently called for the Islamic Republic to end diplomatic ties with Israel.
It is one of the few Arab League governments to hold such relations with Israel.
Attacks by religious groups have increased in the region in past months.
Four French tourists and some troops were killed in the West African nation in December. Fighters allied to the al-Qaeda in the Islamic Maghreb – al-Qaeda's North African branch – said they committed the attack.
This led to the cancellation of the Lisbon-Dakar rally due to safety fears.