Indonesian foreign ministry spokesman Yuri Thamrin said that its envoy would be called back to Jakarta for "consultations" with foreign ministry officials over the matter.
"It is not a permanent recall, but it is important because there are issues that need to be discussed over this incident," Mr Thamrin told a press briefing.
Echoing a statement cleared by the presidential palace, Mr Thamrin said Jakarta was "surprised, disappointed and we deeply deplore this decision".
Australia's envoy to Jakarta, Bill Farmer, was on Thursday summoned to the foreign affairs ministry and told of Indonesia's "disappointment and our dismay", Mr Thamrin earlier told AFP.
The spokesman said Australia's decision to grant temporary visas to 42 of a group of 43 Papuan asylum seekers will damage relations between the two countries.
The Papuans, who include pro-independence activists and their families, have accused Indonesia of "genocide" in the troubled province.
Indonesian Foreign Minister Hassan Wirayuda told reporters that the recall would take place "as soon as possible, as soon as there's a flight that can take our ambassador home," the Detikcom online news agency reported.
Australia has sought to hose down the row, which threatens to become the worst diplomatic crisis between the two neighbours since the 1999 East Timor independence referendum.
Canberra said it remains opposed to independence for the Papua province, and Australian Foreign Minister Alexander Downer said the decision to grant visas was taken at "arm's length" from the government.
"I hope they understand where we're coming from -- we're certainly not in any way changing our position on the recognition of West Papua as part of the Republic of Indonesia," he told ABC radio.
Mr Downer said he is confident the visa decision will not cause long-term damage to relations with Indonesia.
Jakarta complained the decision was based on "one-sided" information from the Papuans only, and Indonesia had not been consulted.
The province of Papua, also known as West Papua or Irian Jaya, is the western half of the island that is also home to Papua New Guinea, and is a former Dutch colony taken over by Indonesia in the 1960s.
Rights groups claim that tens of thousands of people have been killed in the mineral-rich region since separatist violence began in the 1970s.