A number of nations, including Iran's major rival Saudi Arabia, last week cut ties with Qatar, accusing it of funding terrorism, charges it denies.
The land border with Saudi Arabia, through which 40% of Qatar's food comes, has been closed.
Meanwhile, mediators Kuwait said that Qatar was ready to listen to the "qualms" of its neighbours.
A spokesman for Iran Air, Shahrokh Noushabadi, told the Agence France-Presse news agency on Sunday: "So far five planes carrying perishable food items such as fruit and vegetables have been sent to Qatar, each carrying around 90 tonnes of cargo, while another plane will be sent today."
It is unclear whether the food is an aid delivery or a commercial transaction.
Mr Noushabadi said deliveries would continue "as long as there is demand".
AFP also quoted the Tasnim news agency as reporting that three ships with 350 tonnes of food were also set to leave for Qatar.
Iran has also opened its airspace to Qatari flights, following airspace closures by Saudi Arabia, Bahrain and the United Arab Emirates.