Turabi, 77, had obtained permission to travel from the interior ministry but was stopped at Khartoum airport, his office manager Awad Abu Bakr said.
The Islamist head of the Popular Congress Party was released from jail in March, after more than two months behind bars for calling on President Omar al-Beshir to surrender to the International Criminal Court.
The ICC issued an arrest warrant for Beshir in March on charges of war crimes and crimes against humanity in Darfur, accusing him of orchestrating a campaign of murder, torture, rape and pillage.
"Turabi had obtained permission to travel from the interior ministry and a boarding pass, but several security men came and took his passport... and returned to tell him that he was not permitted to leave," Abu Bakr said.
He did not say what Turabi's medical examinations would have involved.
Regarded as one of the driving forces behind the introduction of Islamic sharia law in Africa's largest country in 1983, Turabi was Beshir's one-time mentor.
In 1989, he rallied behind Beshir, then an obscure military man who had just been promoted to general, to overthrow the democratically elected government of his brother-in-law, Sadeq al-Mahdi.
But he lost a protracted power struggle with his protege and was stripped of all his posts a decade later and has since spent repeated spells in jail or under house arrest.