Rouhani had been due to hold talks in Rome on Saturday with Pope Francis as well as Italian counterpart Sergio Mattarella and Prime Minister Matteo Renzi before travelling on to the French capital.
Foreign Minister Mohammad Javad Zarif, who had been due to travel with Rouhani, told state television he would now instead head Iran's delegation to international talks on the Syrian conflict in Vienna.
Deputy Foreign Minister Hossein Amir Abdollahian had been due to lead the Iranian team.
Rouhani sent a message of condolence to French counterpart Francois Hollande on the shootings and bombings in Paris that left more than 120 people dead, Iran's official IRNA news agency reported.
Signup to our newsletter and follow us on Facebook and Twitter!
"In the name of the Iranian people, who have themselves been victims of terrorism, I strongly condemn these crimes against humanity and offer my condolences to the grieving French people and government," Rouhani said.
Zarif said the Paris attacks made the Vienna talks all the more important as world governments needed to work together to fight against the Islamic State group and other extremists.
"We must use the opportunity presented by these crimes to coordinate internationally," he said.
"The Paris events show once again that terrorism and extremism are an international threat and that international cooperation is necessary to fight this phenomenon."
Iran is, with Russia, a key backer of the Syrian regime not only against IS but also against other rebel groups.
It is also a major supporter of Iraq in its war against the jihadists independently of the US-led coalition.