A statement by the president's office on February 25 said Talabani fell ill because of hard work in recent days. The statement says doctors "have asked for more tests and he has gone to Jordan."
"There is no cause for concern," the statement said, but gave no details of his illness.
Deputy Prime Minister Barham Salih told Reuters Talabani left for Amman in the afternoon of February 25 and will be treated at a specialist hospital in Jordan.
Salih said Talabani had a drop in blood pressure and that doctors said he needs further tests.
The president is a former Kurdish guerrilla leader who fought late Iraqi dictator Saddam Hussein for years.
Talabani heads the secular, socialist Patriotic Union of Kurdistan (PUK), one of two parties that dominate the Kurdish enclave that broke away from Baghdad's control after the 1991 Gulf war.
(compiled from agency reports)