"Hon. Mossi assassinated 10.30 in Gihosha", in the east of Bujumbura by, "two criminals in a vehicle," police spokesman Pierre Nkurikiye said on Twitter.
Mossi, a former journalist in her 50s who previously worked for the BBC's Swahili Service, was a member of President Pierre Nkurunziza's ruling CNDD-FDD party.
"The assassination of Hafsa Mossi is a despicable and cowardly act," Nkurunziza tweeted.
"This is an inestimable loss for Burundi, her family and the whole EAC (East African Community)," he added.
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Foreign Minister Alain-Aime Nyamitwe called her death "a great loss for the nation".
Nkurunziza's controversial but ultimately successful bid for a third term last year triggered a deadly crisis that has left more than 500 people dead and driven around 270,000 to leave the country.
Several senior military officers close to the president have been assassinated since the start of the crisis in April 2015, but Mossi, who was not regarded as a party hardliner, is the first senior politician to be killed.
An investigation was swiftly opened.
Louise Mushikiwabo, the foreign minister of neighbouring Rwanda, which has difficult relations with Burundi, spoke on Twitter of a "good woman and a dedicated politician. Rest in Peace my sister!"
France condemned the assassination in a statement, adding that Paris was monitoring closely the "continued violence and human rights abuses in Burundi".
The statement also called for an "extensive dialogue" to help bring about an end to the crisis engulfing the country.
Amnesty International called for an independent enquiry into Mossi's assassination.