"I don't have the details but this is not a practice to be encouraged," Annan told CNN television at the UN on Tuesday.
Thaksin was attending a meeting of the UN general assembly in New York when leading members of Thailand's army launched a coup against him by taking over key government buildings in the south-east Asian country.
Annan said that the coup went contrary to the principles of the UN.
"We as an organisation have always supported governmental changes through democratic means, through the ballot box," he said.
"As the African Union, for example, has indicated they do not support those who come to power through the barrel of a gun."
Annan urged the Thai people to "remain calm".
"Over the past decade or so they have established a solid democracy and institutions under the leadership of the king. And I'm sure they will be able to restore that institution and go back to a democratic system as soon as possible," Annan told CNN.
Matti Vanhanen, the Finnish prime minister whose country currently holds the rotating presidency of the EU, called on Thailand to revert to democracy.
Thailand needed to "revert to democratic order without delay,” the EU presidency said on Tuesday.
"It is highly regrettable that democratic institutions seem to have been taken over by military force," he said.
Other leaders at the UN have voiced their concern over the coup but stopped short of calling on the Thai army to return power to Thaksin and his elected government.
Australia has expressed "grave concern" that the military coup in Thailand posed a threat to Thai democracy.
"We deeply regret the fact that such a coup has taken place; obviously to see democracy destroyed in that way is a matter for grave concern to us," Alexander Downer, the Australian foreign minister, told the Australian national radio by telephone from New York.
"But what we will do as a consequence of it, it's far too early to say."
The Australian government has warned its citizens not to travel to Thailand because of the coup and warned visitors already there to take extreme caution.
The White House said it was monitoring the events closely but was not yet ready to take a public position on events in Thailand.
"The situation at the moment is unclear," said Frederick Jones, a spokesman for the US National Security Council.
"We look to the Thai people to resolve their political differences in a peaceful manner and in accordance with principles of democracy and rule of law."
John Bolton, the US ambassador to the UN said it was still too early to comment but appealed for Thailand's army to respect the country's laws.
"We have press reports and I think for now the important thing is to look for the sustaining of constitutional processes in Thailand," Bolton said.
Thaksin has cancelled his plans to give a speech to the UN general assembly.