The International Paralympic Committee said Bahman Golbarnezhad, 48, suffered cardiac arrest after the incident on a "mountainous stretch" of circuit.
"The ambulance then diverted to the nearby Unimed Rio Hospital in Barra where he passed away soon after arrival," a statement added.
Golbarnezhad also competed at the London Paralympics in 2012.
An investigation into the circumstances of the accident has been launched.
"We're looking to gather as much information as we can and as quickly as possible - it should take a matter of days," said Piers Jones, sports director of cycling's governing body UCI.
The Iranian flag has been lowered to half-mast in the Paralympic Village and a period of silence will be observed during Sunday's closing ceremony.
Masoud Ashrafi, the secretary general of Iran's National Paralympic Committee, said it had requested the body of Golbarnezhad be flown to Iran on Sunday. The Committee also asked for a full report of the incident from the IPC.
Ashrafi added: "He had been cycling for 12 years and he was our best cyclist. He was married and has a wife and one son.