By Agence France-Presse
Around 50,000 people marched in Jakarta on Friday to protest comments made by governor Basuki Tjahaja Purnama, with clashes erupting between police and demonstrators just metres from the presidential palace and city hall.
"Current development has required the President to stay in Indonesia," a statement released on Saturday by the foreign ministry said.
Widodo visited Australia in 2014 for the G20 shortly after being elected as president, but this month's trip would have marked his first official bilateral visit.
The statement added that Widodo had called Australia's Prime Minister Malcolm Turnbull to inform him that the trip, scheduled for 6-8 November, would be delayed.
The protest in Indonesia's capital was triggered by accusations that Purnama, better known by his nickname Ahok, insulted Islam by criticising opponents who used Koranic references to attack him ahead of an election in February.
Purnama apologised for the remarks, but his opponents have built a groundswell of support calling for his arrest and incarceration under Indonesia's tough blasphemy laws.
Demonstrations were initially peaceful but turned ugly in the evening when protesters refused to go home, resulting in thousands of hardliners clashing with police, setting vehicles ablaze and hurling bottles and rocks at officers, injuring several.
The Indonesian police have arrested 10 people thought to have instigated the violence.