Australian Prime Minister Tony Abbott said it "cannot be business as usual" with Indonesia, after the latter executed two Australians for drugs trafficking.
Andrew Chan and Myuran Sukumaran were among eight people executed by firing squad early on Wednesday.
Australia promptly withdrew its ambassador and anger over the executions has emerged in the form of a social media campaign to boycott the South East Asian country.
Calls for Australians to boycott Indonesia have prompted a heated debate on Twitter, with some users reporting they would cancel their trips, while others dismissed the idea.
Qantas chief executive Alan Joyce told the Australian newspaper there had been few signs of a boycott at the airline.
"At the moment it doesn't look like there's been any impact so far on the demand," said Joyce. "A lot of customers recognise that boycotting Bali is only going to damage the local population."
John Guscic, chief executive of the Australian travel booking website Webjet, told News.com that there had been no boycott so far.
"Over the last four weeks bookings to Bali have been ahead of trend. There is an underlying trend of 37% in bookings to Bali but in the last four weeks it has been 43%," he said.
Australians make up Indonesia's third biggest tourism market, while the two countries have strong trade links.
Tourism has become an increasingly important part of Indonesia's overall economy, employing 10 million people and contributing 4% to the country's gross domestic product in 2014.