“At the request of the Iraqi government, we have closed our land and air borders” with Iraqi Kurdistan, foreign ministry spokesman Bahram Ghasemi said at a press conference.
The referendum is “illegal and illegitimate,” he added.
Iran had already announced on Sunday that it was stopping all flights to and from Iraqi Kurdistan in response to the vote.
President Hassan Rouhani spoke overnight with Iraqi Prime Minister Haidar Al-Abadi, saying: “The Islamic republic of Iran fully supports the central government of Iraq.”
The referendum went ahead on Monday despite strong opposition from Baghdad and its neighbors, as well as Western governments including the United States.
Iran fears the vote could encourage separatists in its own Kurdish region, and said last week that independence could mean an end to all of border and security arrangements.
Iranian security forces have faced regular attacks by militant Kurdish separatists, primarily based across the border in Iraqi Kurdistan.