Ali Larijani had been invited by his Turkish counterpart to take part in a parliamentary conference in Istanbul.
The Iranian speaker cancelled his trip on Wednesday evening, hours after Turkey launched the military operation in Syria.
Iranian authorities, including President Hassan Rouhani, had urged the Ankara government to avoid taking military action in Syrian territories and reconsider its decision.
President of Turkey Recep Tayyip Erdogan says the offensive, which began with air raids on Tuesday, is aimed at removing Kurdish-led forces from the border area and creating a “safe zone” to which millions of Syrian refugees can be returned.