The embassy told AFP the bomb exploded as a single armoured car with four French guards on board was passing by and that no one inside was hurt.
"The bomb targeted a passing French diplomatic convoy. Four Iraqi guards protecting the convoy were hurt, and three people passing by were also wounded," an interior ministry official told AFP earlier.
A medical source at Ibn Nafis hospital said it had received seven wounded Iraqis, among them four guards.
The bomb struck near the French ambassador's residence in the Mesbah district of southern Baghdad, and an embassy vehicle damaged by the explosion was left at the site, an AFP journalist said.
"A single armoured vehicle carrying four French embassy guards was damaged by a roadside bomb at 8:17 a.m. (0517 GMT)," said Denis Gauer, the French ambassador who recently arrived in Baghdad to take up his post.
"No one in the car was hurt and there is no indication the bomb was especially targetting this vehicle," he told AFP.
A witness said the bomb appeared to have been placed under a parked vehicle.
"A bomb under a parked car exploded as soon as a blue 4x4 vehicle from the embassy arrived. The embassy car was hurled forward a few feet," said Abu Hassan, who witnessed the explosion.
Violence has plummeted in Iraq since its peak in 2006 and 2007, when tens of thousands were killed in clashes between Sunni and Shiite Arabs and insurgent attacks. But bombings and kidnappings remain common.
Official figures put the death toll from attacks in May at 177, most of them killed by roadside bombs or with silencer-fitted handguns.
In other attacks in Baghdad and elsewhere in Iraq, at least three people were killed and nine wounded by gunmen and bombs on Monday, an army colonel and interior ministry sources said.
The dead included the mayor of the town of Al-Shar in central Baquba province and a policeman in Baghdad, both killed by gunmen, they added. A car bomb also killed a civilian in a northeastern Baghdad district.
In the northern province of Kirkuk, gunmen kidnapped a 37-year-old businessman on Monday and and an 81-year-old optometrist the day before, a police source said.
Kidnappings are common across Iraq, especially in multi-ethnic and multi-religious Kirkuk.
The rise in violence comes with only months to go before US troops, in Iraq since the 2003 invasion, are due to complete a pullout under the terms of a bilateral security pact.
Monday's attack comes as eight US soldiers have been killed on duty so far this month, and a June 14 raid by gunmen against government offices in the central city of Baquba in which seven people were killed.
Private security firm AKE Group said this month that attacks have been on the rise since the start of the year, with violent incidents averaging more than 10 a day in May, up from four to five a day in January.