The BBC reported in Antananarivo that police opened fire after demonstrators who support former President Marc Ravalomanana barricaded roads to protest the closure of two radio stations. Cars were set on fire close to government buildings.
Tear gas also was used on protesters who had fled to the city's main hospital where doctors said one person was dead of head injuries, the British network said.
Ravalomanana resigned in March in the face of a coup led by opposition leader Andry Rajoelina.
Rajoelina, who has said he intends to hold presidential elections in October 2010, has issued a warrant for Ravalomanana's arrest.
Ravalomanana, now in Johannesburg, South Africa, said he plans to return to Madagascar in the next few weeks.
He said holding elections this year is "the only way out of the crisis."
In the wake of the coup, Madagascar was suspended from the African Union and the Southern African Development Community.
Ravalomanana, who maintains he is still the democratically elected and constitutional president, said Monday he has appointed Manandafy Rakotonirina as his new prime minister, AllAfrica.com reported.
Ravalomanana said he "will work with all parties interested in a peaceful outcome, that adhere to the Constitution, the rule of law, and democracy."