Shells could be heard exploding at the base even though it was deserted, local residents told news agencies by phone Sunday.
The soldiers had fled, some shedding their uniforms, leaving Arab militiasfrom the Bérabish community to defend the town, they said.
Map of Mali
Al Jazeera television reported that the town, whose population is mainly ethnic Arab, had fallen to the rebel National Movement for the Liberation of Azawad (MNLA), which wants a Tuareg homeland in the north of the country.
On Saturday the army quit the largest town in the north, Gao, leaving it to the MNLA which has already captured Kidal.
Timbuktu, a historic city that is on the Unesco World Heritage list, is 800 km north of Bamako and 300 km west of Gao.
In Bamako coup leader Captain Amadou Sanogo on Sunday agreed to reinstate the constitution suspended after he toppled President Amadou Toumani Touré and launch a national dialogue.
The move came ahead of a midnight deadline to do so from the west African states grouping Ecowas.
Oponents of the military rulers seized on the setbacks in the north to call on the military to accept the plan on Saturday.
“There is fire everywhere,” union leader Siaka Diakité said in a statement Saturday. “Mali cannot fight on all fronts at once … Let’s set aside personal quarrels.”
Ecowas had given the military junta until midnight Sunday to accept its plan, threatening to close the borders, cut off funding from the West African Central Bank, freeze the assets of junta members and ban them from travelling abroad.