Iran stands by Syria in row over missiles
"The internal crisis in Syria cannot be solved through the deployment of such weapons," said Mr Larijani.
Turkey's request follows several incidents in which violence has spilled across the border from the civil war in Syria, with mortar rounds falling a short distance inside its territory.
Patriots would be useful in intercepting ballistic missiles – a much more serious but still hypothetical threat. NATO has said it will consider the request "without delay."
The Syrian foreign ministry also criticised the Turkish move.
Mr Larijani, who met Syrian president Bashar Assad in Damascus earlier yesterday, said Iran was seeking a peaceful solution to the war in Syria.
"The difference between us and the others when it comes to Syria is that the others want to impose democracy through weapons," he said, adding: "Iran cannot accept or support such a way. I don't think democracy can be achieved through rocket propelled grenades."
Iran is Assad's strongest ally in the region and anti-government activists accuse Tehran of sending both weapons and fighters to help Assad's regime.
Syria's conflict erupted in 2011 with an uprising against Assad's regime, but quickly morphed into a civil war that has since killed more than 40,000 people, according to activists.