The leaders of Australia, the US, Japan and India were all scheduled to meet in Sydney on May 24 for a Quad meeting.
Mr Biden was due to address the federal parliament in Canberra the day before.
Prime Minister Anthony Albanese said he took a call from Mr Biden early on Wednesday morning.
"The president apologised that he would now have to postpone this visit because of the unfolding difficulties he is facing in his negotiations with the US Congress over the US government debt ceiling," Mr Albanese said.
"These negotiations are scheduled to enter their critical and concluding phase during the last week of May.
"Regrettably, this conflicts with the President's visits to Sydney and Canberra - including the Quad Summit scheduled for 24 May."
Mr Albanese said the two leaders had agreed to reschedule his visit to Australia as soon as possible.
Earlier, White House national security spokesman John Kirby confirmed Mr Biden was going to Japan for the G7 summit at the end of the week.
He noted Mr Biden would meet the Quad leaders - including Mr Albanese, Japanese Prime Minister Fumio Kishida and Indian Prime Minister Narendra Modi - at the three-day G7 summit in Hiroshima.
Mr Albanese said the government was now in discussions with Tokyo and Delhi about Prime Minister Kishida's and Prime Minister Modi's travel.
"Once those discussions are concluded, we will make a further announcement on their travel," he added.
"In the meantime, I look forward to meeting with both prime ministers and the president at the G7 Summit in Hiroshima on 20-21 May."
The wrangling in Washington between the White House and Congress Republicans revolves around a deal to raise the US government's $US31.4 trillion ($A46.9 trillion) debt ceiling and avert an economically catastrophic default.
It would have been the first visit by a US president to Australia in almost a decade and the fifth time a US president had addressed MPs and senators.
Opposition Leader Peter Dutton said the president's cancellation was disappointing but understandable.
"There are domestic issues that the president has to attend to, and he'd be a welcome guest into our country at any time," he told Sky News on Wednesday.
"This was going to be an opportunity on a bipartisan basis to welcome him to our country. The AUKUS arrangement is historic."
Mr Dutton said he hoped there was the possibility Mr Biden could attend the Quad meeting virtually.
"We're more used than ever to speaking to people down the television screen and there will be plenty of opportunity for him, I suspect, to join the Quad and all of those logistics will be put in place because it's important to turn the meeting go ahead," he said.
"The Quad is incredibly important for our region, and they're important partners, and I'm sure the US president can join via video."
The Quad is not a military alliance and was set up to counter Chinese influence in the region.
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