Ahmadinejad had been officially invited to and was scheduled to attend the annual commemoration ceremony for Mevlana Jalal ad-Din Rumi, the 13th century Persian Muslim theologian.
He was also to have met Turkish Prime Minister Recep Tayyip Erdogan, Iranian media reported.
But Ahmadinejad cancelled his visit because of a "busy schedule," Mehr news agency quoted the head of his international office, Mohammad Reza Forghani, as saying.
The cancellation came a day after Iranian Foreign Minister Ali Akbar Salehi warned Turkey over plans to deploy NATO-controlled US-made Patriot missiles along its border with Syria amid tensions with President Bashar al-Assad's regime.
Deploying the missiles in Turkey is a "provocative" action which could have "uncalculated" results, Salehi said on Sunday.
On Saturday, the joint chief of Iran's armed forces General Hassan Firouzabadi warned that the Patriot deployment was part of a plot to "create a world war."
Relations between Iran, Assad's main regional ally, and Turkey, a vocal opponent of the Damascus regime, have been strained over the conflict in Syria.
Some Iranian officials have accused Turkey of arming Syrian rebels