Saad Al-Hayyani, Iraq's ambassador to Jordan, told The Associated Press Talabani was suffering from "general fatigue and exhaustion and he needs medical examination to determine what is causing that."
The Iraqi president was taken to Amman's King Hussein Medical City, a military hospital in a police escorted motorcade.
Before Talabani's arrival a doctor from the hospital said the Iraqi leader would "be admitted to the hospital's heart center."
The center was chosen, the doctor said, because it "Has sophisticated and modern equipment to check his condition," and did not mean Talabani has a heart condition or suffered a stroke.
Earlier a doctor in Sulaimaniyah, Talabani's hometown, told AP that the president was unconscious when an ambulance rushed him to a hospital there.
"After his condition stabilised, the doctors advised him to go to Jordan for a complete check up," he said on condition of anonymity.
A senior member of Talabani's Patriotic Union of Kurdistan (PUK) told Agence France-Presse that the Iraqi president was suffering from kidney problems.
He said: "[Talabani] has an excess of urea. He was treated for several hours in hospital here in Sulaimaniyah, then he was flown from the airport to Amman."
Talabani, a Kurd, appeared in public on Saturday in Sulaimaniyah where he met with Zalmay Khalilzad, the US ambassador, and Massoud Barzani, leader of the autonomous Kurdish region in northern Iraq.
Barham Saleh, Iraq's Kurdish deputy prime minister, told reporters that Talabani was overworked.
"This morning President Talabani's heath was not stable and he underwent treatment. When his condition improved he was transferred, at 8:30pm (17:30 GMT). He was flown to Amman," Saleh said.
Saleh said members of Talabani's immediate family accompanied him to Amman.
The deputy prime minister told Reuters that the president had "had a drop in blood pressure".
Talabani heads the secular PUK, one of two parties that dominate the Kurdish enclave that broke away from Baghdad's control after the 1991 Gulf war.
A former guerrilla leader who fought Saddam Hussein for years, Talabani became Iraq's first Kurdish head of state.