Adams is on holiday in Tonga with her partner Gabriel Price, and the pair were planning to fly to the island of 'Eua on the aircraft over the weekend.
On a photo they posted just before boarding, the caption said: "...the real Tonga Airlines on their way to 'Eua only to find out the breaks [sic] don't work as the plane started to slide off the runway ... thank goodness everyone was safe and no one got hurt."
It drew comments from others, including one that said: "Only in Tonga can the Olympic gold medallist go home to relax and almost ends up in a plane crash."
Adams wrote on her Instagram account: "Back in Tonga cause [sic] problems with brakes haha so waiting on eta for our flight zzzzz."
In August 2013, the Ministry of Foreign Affairs and Trade posted a travel advisory in relation to the aircraft, which was a gift from China.
"This aircraft has been involved in a significant number of accidents in the last few years," Mfat said at the time.
"Travellers utilising the MA60 do so at their own risk."
The advisory also said the MA60 was not certified to fly in New Zealand or other comparable jurisdictions and would not be allowed to do so without a thorough certification process under Civil Aviation rules.
Foreign Affairs Minister Murray McCully said then that the aircraft had been the subject of "serious concerns" amongst aviation experts.
In its latest advisory, the ministry said the Tongan Government "is working closely with the Pacific Aviation Safety Office on a major overhaul of aviation safety".
While in Tonga, Adams and her partner were invited to a New Year's Day reception hosted by the King of Tonga Tupou VI.
Tongan media reported that the shot putting great was the star of the reception, which was attended by about 200 guests including the new Prime Minister, 'Akilisi Pohiva.
She was dressed in a bright red island-style pula taha (two-piece dress) with the traditional ta'uvala mat wrapped around.
Adams could not be reached for comment.
