The dam, which is several years from completion, was planned to be the world's 15th tallest at 152m (500 feet) high.
The campaign against the project brought together conservationists, environmentalists, Kachin activists and the political opposition.
Their objections ranged from the lack of public consultation to the potential environmental impact of a project that would have created a reservoir of some 766 sq km (300 sq miles) - about the size of Singapore - and forcibly displaced thousands of ethnic Kachin villagers, our correspondent says.
"The president sent a message comprising 10 points to the parliament this morning. One of them said that the construction of the dam on the Irrawaddy will be shelved during the term of his government," one official at parliament was quoted by Reuters news agency as saying.
"He said that his government, being born out of people's desire, has to act according to the desire of the people," said the official, who declined to be named because he was not authorised to speak to the media.
The editor of the Irrawaddy News website, Burmese Aung Zaw, based in northern Thailand, told the BBC the decision was unexpected.
"It was a welcome surprise for everybody, inside and outside of Burma," he said.
"The people [are] really happy and welcome the decision made by President Thein Sein because it wasn't only [Aung San] Suu Kyi, let me remind you of that.
"It's the population, the whole Burmese who feel they belong to the culture heritage of the Irrawaddy river. They welcome the news."
The vast majority of the electricity produced on the dam would benefit China, and the dam had served to inflame growing anti-Chinese sentiment in Burma, our correspondent says.
Beijing is investing vast sums in a series of big infrastructure projects aimed at exploiting Burma's rich natural resources and geographic position in the region, she says.
There has as yet been no official reaction from China to the unusual step taken against it by its isolated ally.Burma's president has suspended construction of a controversial Chinese-backed hydroelectric dam.
In a letter read out in parliament on Friday, Thein Sein said the $3.6bn (£2.3bn) Myitsone dam was contrary to the will of the people and lawmakers.
Pro-democracy leader Aung San Suu Kyi recently joined the anti-dam campaign.
The suspension is being seen as a rare victory for social and political campaigners, says the BBC's Rachel Harvey in Bangkok.
It appears to be further evidence of the new leadership's desire to seek legitimacy by being more open to public opinion since the army nominally handed over power to a civilian authority in March.
Burma lobby groups will still be very wary - President Thein Sein has only said he is suspending the dam's construction for the term of his office - but this is perhaps the most concrete sign yet of changing attitudes, our correspondent says.
Spectrum of oppositionThe Myitsone dam project was being developed jointly by Burma and China at the head of the Irrawaddy river, the confluence of the Mali and N'Mai rivers in Kachin state, in an area currently the scene of conflict between government forces and ethnic minority insurgents.
