The bus had entered Turkey from Bazargan border crossing and was heading to the city of Van in eastern Turkey when it came under attack.
Iran's Consul-General in Erzurum Hossein Qassemi told IRNA that the Iranian tourist was shot in the head.
The report said the Iranian national succumbed to the wounds after being taken to hospital.
Qassemi said three other people were critically injured in the attack, and added that other passengers of the bus are in good health and have been transferred to Van.
The development came a week after two passenger Tehran-Ankara trains were attacked in Turkey.
The services, which run between Iran and Turkey, were hit by blasts from remotely detonated landmines, in attacks Turkish officials blamed on Kurdistan Workers' Party (PKK) militants.
Following the attacks Iran cancelled all trains to the Turkish capital in a bid to ensure the safety of passengers.
Iran’s Rail Transportation Company (Raja) announced in a statement at the time that it has cancelled its train services to the neighboring country last Thursday, and will not dispatch any train to Ankara until Turkish authorities make official comments.