Mr Albanese is due to fly to Singapore on Thursday afternoon to deliver what has been billed the most significant foreign policy speech of the year at the Shangri-La Dialogue.
Singaporean Prime Minister Lee Hsien Loong posted on Twitter he had tested positive to COVID-19 but felt fine.
He said doctors told him it was a "COVID rebound", which happened in five to 10 per cent of cases and was infectious.
"The doctors have advised me to self-isolate until I test negative," Mr Lee wrote.
Mr Albanese was to hold a bilateral meeting with Mr Lee, but it is expected he will now meet Acting Prime Minister Lawrence Wong.
Mr Wong is considered the likely successor to Mr Lee when he steps down before the 2025 election.
Mr Lee visited Australia in 2022, when the leaders signed a green economy deal, which will be further discussed in Singapore as businesses and government seek to activate it.
Mr Albanese will also make his first trip as leader to Vietnam over the weekend, meeting the country's senior leadership.
Trade Minister Don Farrell, who recently returned from Vietnam, said the country of more than 100 million people offered many opportunities.
"(It has) a rising middle class and is very keen to move from the status of a developing country to the status of a developed country by 2045," Senator Farrell said.
He said tourism, education and alcohol exports were potential areas of growth.
"I was blown away by the number of senior people I met, both in business and in government, who had actually either been educated in Australia or educated by Australian universities in Vietnam, or who had children who were currently in Australia," he said.
"I think one of the greatest opportunities is in that education space, either more Australian universities setting up in either Ho Chi Minh or Hanoi or sending more students."
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