"We are on the Al-Qaeda track," the source said. "The Tunisian we have arrested told us he belongs to Al-Qaeda."
Police said the man belonged to Al-Qaeda in the Islamic Maghreb (AQMI), which experts believe has bases spread across Algeria, Mauritania and Mali.
Two Malians were slightly wounded by the blast.
The source said the man came from "a Katiba", a camp of Islamist fighters in the Sahara, but he did not seem to be an important member of the organisation.
The French foreign ministry confirmed the blast, but spoke of only one person being wounded.
The ministry's deputy spokesperson Christine Fages said: "There was an explosion that was not accidental in front of the French embassy which very slightly wounded one person of Malian nationality among its staff.
"An inquiry is under way," she added, refusing to make any further comment when asked if the French embassy had been specifically targeted and if the blast might be linked with the detention of French hostages in northeast Mali by the north African branch of Al-Qaeda.
AQMI is holding in the Sahara five French nationals, a Togolese and a Malagasy who were kidnapped in September at Arlit, a strategic mining site of French nuclear giant Areva in north Niger.
In August 2009 a young man blew himself up in Nouakchott, capital of neighbouring Mauritania, near the French embassy lightly injuring two French gendarmes and a Mauritanian woman. AQMI claimed the attack carried out by a Mauritanian suicide bomber.
AQMI later again designated France as a target after a Franco-Mauritanian operation last July 22 against an Al-Qaeda base in Mali aimed at freeing a French hostage, Michel Germaneau, 78. But the operation failed and AQMI later announced it had killed the hostage.
In Bamako the French high school announced late Wednesday that it would be closed on Thursday.