In a television announcement, a spokesman for the plotters said Niger’s constitution had been suspended and all state institutions dissolved.
The country was now being led by a group called the Supreme Council for the Restoration of Democracy (CSRD), the spokesman said.
President Mamadou Tandja is believed to be in captivity at a military barracks.
Reports say government ministers are also being held.
Making the announcement on television, the spokesman for the coup leaders, wearing a military uniform, was surrounded by a large group of soldiers.
He called on the people of Niger to “remain calm and stay united around the ideals postulated by the CSRD”, to “make Niger an example of democracy and good governance”.
“We call on national and international opinions to support us in our patriotic action to save Niger and its population from poverty, deception and corruption,” he added.
A newsreader on Niger television said the country’s borders had been closed and a curfew was now in force.
Tensions have been growing since last year in the uranium-rich nation.
Mr Tandja was widely criticised when he changed the constitution in August to allow him to stand for a third term.
A BBC correspondent said earlier that tanks were firing and witnesses reported seeing injured people being taken to hospital.
The exchange of gunfire has been between soldiers but it is confusing and one cannot tell one side from another. I saw tanks being fired and soldiers on the streets using machine guns.
The area near the presidential palace is where the business of government takes place and at least four military barracks are based there.
People have fled the area and some civil servants have locked themselves inside their offices.
Earlier, smoke could be seen from the roof of the office where President Mamadou Tandja was holding his cabinet meeting.
An unnamed French official told AFP that the president had been seized.
“All I can say is that it would appear that Tandja is not in a good position,” he told the news agency on condition of anonymity.
Soldiers captured Mr Tandja while he was chairing his weekly cabinet meeting, a government source told the BBC.
AFP later reported an official as saying Mr Tandja was possibly being held at a military barracks about 20km (13 miles) west of Niamey.
A witness told the news agency that the bodies of three soldiers had been taken to a military mortuary.
The situation in Niamey remains unclear – there has apparently been no large-scale deployment of military personnel.
The government and opposition have been holding on-off talks since December – mediated by the regional body Ecowas – to try to resolve the country’s political crisis.
Ecowas has told the BBC that it is closely following developments in Niger.
The organisation’s political director, Abdel-Fatau Musah, said that, if needed, Ecowas would be in the country as quickly as it could to ensure order was maintained and constitutional order restored as soon as possible.
Mr Musah said that while Ecowas would never recognise a military takeover, it would maintain a constructive engagement with those in authority in Niger.
Mr Tandja, a former army officer, was first voted into office in 1999 and was returned to power in an election in 2004.
Niger has experienced long periods of military rule since independence from France in 1960.
It is one of the world’s poorest countries, but Mr Tandja’s supporters argue that his decade in power has brought a measure of economic stability.
Under his tenure, work has begun on the world’s second-biggest uranium mine, and energy deals have been signed with Chinese firms. BBC