A US military statement on Thursday said the death "appeared" to be from natural causes.
Major-General Abed Hamed Mowhoush, a former air defence commander, died on Wednesday morning, said the statement issued from the western town of al-Qaim in the troubled Syrian border region.
"Mowhoush said he didn't feel well and subsequently lost consciousness. The soldier questioning him found no pulse, then conducted cardiac and pulmonary resuscitation and called for medical authorities," the statement said.
"A surgeon responded within five minutes to continue advanced cardiac life support techniques, but they were ineffective. According to the on-site surgeon, it appeared Mowhoush died of natural causes," it said.
The statement said that its forces were cooperating with local tribal and religious leaders to "properly treat and transfer the body to their control while verifying the cause of death" which was "currently under investigation".
The general was a member of the Mahalowi tribe from the middle Euphrates valley north and west of the Iraqi capital, a bastion of support for Saddam Hussein.
The area around al-Qaim and the border town of Husaybah further west has witnessed intense resistance against US troops.