The non-binding referendum, which was due to take place on Sunday, would have asked Hondurans whether they approved of holding a poll on constitutional change alongside general elections in November.
The president fired the armed forces chief of staff last week after he refused to help him organise the vote.
The HRN radio station reported that Zelaya had been sent into exile, citing unidentified "trustworthy sources". Other reports suggested that he may have headed to Venezuela.
"We're talking about a coup d'etat," Rafael Alegria, a union leader and ally of Zelaya, told Honduras' radio Cadena de Noticias. "This is regrettable."
The streets of Tegucigalpa were largely empty of traffic, other than the tanks and lorries of the army, after reports on local radio urged the city's residents to stay inside.
But a large group of Zelaya's supporters gathered outside the presidential palace, shouting insults at the soldiers that were surrounding the building and setting fires in the streets.
"They kidnapped him like cowards," Melissa Gaitan, an employee of the official government television station, said.
"We have to rally the people to defend our president."
The supreme court and the attorney-general have said that the vote was is illegal because the constitution bars changes to some of its clauses, such as the ban on a president serving more than one term.
Their decision has been backed by the military and congress.
Colin Harding, an expert in Latin American politics, told Al Jazeera that Zelaya had apparently overestimated his own power in pushing for the referendum.
"He has no support in within his own party, he is opposed by congress, he is opposed by the judiciary and the military, who are not the power they used to be but have lined up against Zelaya ostensibily in defence of legality," he said.
However, many union, labour and farm movements support the referendum, which Zelaya says is aimed at improving the lives for the nearly three-quarters of Hondurans who live in poverty.
Oscar Hendrix, a youth movement leader in the northwestern city of San Pedro Sula, said that the military had burned the ballot papers that had been distributed in defiance of the supreme court ruling.
"This is unconceivable, this is one of the fundamental rights of the people," he told Al Jazeera.
Hendrix said that there would be protests against the military's actions.
"We are analysing right now whether we are going to do something here or whether we are all going to mobilise to the capital city," he said. "We will stand up for our rights."
Zelaya was elected for a non-renewable four-year term in 2006 as a member of one of Honduras's established conservative political parties, but since taking power he has moved to the left, aligning himself with Hugo Chavez, Venezuela's president.