Taufik Kiemas, a prominent millionaire businessman and politician, was admitted to a private hospital in Perth, Western Australia, on Wednesday.
An Indonesian spokesman in Perth denied Mr Kiemas had suffered a heart attack and said the tests were routine.
Mr Kiemas has a history of heart problems and on Tuesday was admitted to a Jakarta hospital with chest pains.
President Megawati did not accompany her husband to Australia, but earlier in the week she cancelled some official business to be with him. He is now staying with consulate staff in Perth.
Key figure
Dr Aulia Sani, said Mr Kiemas goes to Perth every five months. He is also said to be a regular patient at the Jakarta's Harapan Kita hospital.
Megawati Sukarnoputri married Taufik Kiemas, her third husband, in 1973. A legislator, he is regarded as being an influential figure within Megawati's party, the Indonesian Democratic Party of Struggle.
He is thought by many to have been instrumental in the fall of former President Adurrahman Wahid and the subsequent rise to power of his wife.
As the son of a devout Muslim who supported Islamic parties, Mr Kiemas is believed to have worked to strengthen Megawati's ties to the Islamic establishment.
But Mr Kiemas has also been the subject of media allegations of questionable business deals which he has strongly denied and refuted by publishing a list of his financial assets.
A student activist in the 1960s, he spent three years in prison for defending the rights of his future wife's father, President Sukarno, who was forced from office by Suharto in 1967.