A crowd in the village square pleaded in vain with the militants to spare the man, Reuters news agency reports.
Northern Mali has been overrun by Islamist and Tuareg rebels following a coup in Bamako in March.
The Islamists have vowed to implement strict Sharia law, despite strong opposition from the local Muslim population.
Last week, a couple who had s*x outside marriage were stoned to death in the town of Aguelhok, controlled by the Islamist group Ansar Dine.
The group has also destroyed ancient shrines in Timbuktu, denouncing them as promoting idolatry.
Mali's weak interim government said the amputation in Ansongo - carried out by the Movement for Oneness and Jihad in West Africa (Mujao) group - was a "vile act".
Military intervention in the north was now inevitable, it said in a statement.
Mujao official Mohamed Ould Abdine said the amputation was in accordance with the "law of God", the AFP news agency reports.
"Sharia demands it," he said.
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A local government official said dozens of people saw the amputation, AFP reports.
"There was a lot of blood when the hand was cut. It was the hand of a thief who stole a motorbike," he said.
On Sunday, scores of protesters in the main regional town of Gao, about 100km (60 miles) from Ansongo, prevented Islamists from carrying out an amputation.
Mr Abdine said the sentence had only been postponed and would be implemented.
Officials from the West African regional body, the Economic Community of West African States (Ecowas), the African Union and the United Nations have been meeting in Bamako to discuss military intervention in the north.
They hope to come up with enough details for the deployment of a force to win the backing of the UN Security Council, which has so far refused to endorse military intervention in Mali, the BBC's West Africa correspondent Thomas Fessy says.
The Islamists took power in alliance with Tuareg rebels fighting for a separate state, but the two groups have since fallen out.
