The White House said it was “logistically… not possible” to go ahead with the trips to Malaysia and the Philippines at the end of his tour.
But he would still be attending regional summits in Indonesia and Brunei, the White House added.
The US government has partially shut down after the two houses of Congress failed to agree a new budget.
More than 700,000 federal employees face unpaid leave, and national parks, museums and many buildings are closed.
Mr Obama on Tuesday vowed not to allow Republicans to undermine his signature healthcare legislation as a condition to restart the US government.
“They’ve shut down the government over an ideological crusade to deny affordable health insurance to millions of Americans,” he said at the White House.
“In other words, they demanded ransom just for doing their job.”