Barack Obama will miss two summits, including the Asia-Pacific Economic Co-operation (APEC) meeting in Indonesia.
The decision was made due to the “difficulty in moving forward with foreign travel in the face of a shutdown”, the White House said.
The US government closed non-essential operations after the two houses of Congress failed to agree a new budget.
Barack Obama called Indonesian President Susilo Bambang Yudhoyono on Friday morning and expressed his regret for the cancellation.
The visit has not been rescheduled.
Secretary of State John Kerry will attend the APEC gathering and the East Asia summit in Brunei in Barack Obama’s place, the White House said.
“The cancellation of this trip is another consequence of the House Republicans forcing a shutdown of the government,” the White House said in a statement.
“This completely avoidable shutdown is setting back our ability to create jobs through promotion of US exports and advance US leadership and interests in the largest emerging region in the world,” the statement added.
Barack Obama had been due to begin a four-nation Asian trip on Saturday, heading to Bali and Brunei for regional summits before travelling on to Malaysia and the Philippines.
On Wednesday, the White House had said Barack Obama would postpone his trips to Malaysia and the Philippines because of the US government shutdown, but maintained that he would travel to Indonesia and Brunei.
The US government began a partial shutdown earlier this week after Republicans refused to approve a budget, saying they would only do so if funding for President Barack Obama’s healthcare reforms was delayed.
On Friday, Democrats and Republicans appeared no closer to resolving the feud.
The US also faces running out of money and defaulting on its debt if there is no agreement to raise government borrowing limits later this month.
Christine Lagarde, managing director of the International Monetary Fund (IMF), said on Thursday that a failure to raise the US debt ceiling would be a far worse threat to the global economy than the current shutdown.
She said it was “mission critical” that the US agrees a new debt limit.
Christine Lagarde’s comments were echoed by the US Treasury.
It said a debt default could lead to a financial crisis as bad as 2008 or worse.
Meanwhile, the impact of the shutdown was being felt across the country.
The National Transportation Safety Board did not send investigators to a deadly church bus crash in Tennessee that killed eight people and injured 14 others.
The Labor Department also said it wouldn’t release the highly anticipated September jobs report on Friday because the government remains shuttered.
With Tropical Storm Karen bearing down on the Gulf States, the website of the National Oceanic and Atmospheric Administration (NOAA), carried a message saying: “Due to the Federal government shutdown, NOAA.gov and most associated web sites are unavailable.”
It referred visitors to the National Weather Service.
However, the Federal Emergency Management Agency (FEMA) recalled workers to help prepare for the storm.
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