The army is investigating a complaint by an Indonesian special forces officer, who was offended by training materials at an Australian base.
Indonesia's military unit has trained alongside Australian special forces for years, but now diplomatic relations appear to be in the firing line.
It's believed a Kopassus soldier was offended by training material at an Australian special forces base late last year and raised it with the Indonesian military's hardline commander, General Gatot Nurmantyo.
Australia's Defence Minister Marise Payne has confirmed, as a result, Indonesia has severed some military ties.
"They have raised these concerns, they've taken the steps that they've indicated that they think are appropriate. I'd have to say at this point although some activities have not occurred others have. The Chief of the Indonesian airforce visited Australia in December."
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Despite assurances the relationship remains strong - training exercises and an upcoming visit by Indonesian defence students have been cancelled.
It's believed the Kopassus soldier was offended by materials regarding Indonesia's involvement in West Papua and a piece ridiculing Pancasila - Indonesia's founding principles.
"Certainly we have indicated our regret that this occurred and that offence was taken. I think that's appropriate when a significant counterpart raises concerns with you no matter who it is. We obviously work very broadly regionally and internationally and we should endeavour to ensure the material we use is culturally appropriate, is to the point, not gratuitous"
Indonesian President Joko Widodo says the country's decision is one of principal.
He told reporters, he believes the relationship between Australia and Indonesia will remain strong.
"I think our relationship with Australia will remain good but on an operational level we need to deliver the message (to Australia) so the situation does not escalate (in the future)."
General Gatot Nurmantyo, has told reporters in Jakarta, it was his decision to suspend military cooperation.
"The materials include content about East Timor, saying that 'Papua needs to be independent', and mock the founding principles of Indonesia as 'Pancagila', meaning crazy in Indonesian. And all the five articles of Pancasila are incorrect, so I have withdrawn the teachers and stopped the program for now."
But retired Army commander Jim Molan, who spent five years in Indonesia, says over time the tension will ease.
"I think it's a storm in a teacup and I think it will pass and I think the main reason it will pass is because the Minister for Defense over there seems to have already calmed things down a bit."
Indonesian Politics Expert Greg Fealy points out that the Indonesian General is suspicious of Australia.
"It's nothing new and his statements are causing increasing problems for President Jokowi because a number of the countries being mentioned by the General are not really happy about it so that's one of the things that we await to see the governments response on."
Indonesia's military is one of the biggest in South-East Asia.
Australia's ties to the mostly Islamic nation go much further than defence.
But vital trade, counter-terrorism and intelligence links have apparently been unaffected.
Experts say there's never been a cancellation of suspension of counter-terrorism training or the intelligence that backs it up.
It's also expected that sharing of intelligence on people-smuggling will continue.
Defence Minister Payne says the Australian Army is close to finalising its investigation into the incident.
"That inquiry is underway it has had to receive information from the Australian side from the Indonesian side to be fair I think you would also appreciate that we have also had the Christmas and New Year period as well but it is very close to finalisation."
