The United States and Israel launched airstrikes on Iran nearly two weeks ago, killing the Islamic Republic's supreme leader, leading to a region-wide conflict in the Gulf.
"Considering that this corrupt regime has assassinated our leader, under no circumstances can we participate in the World Cup," the minister told state television.
The World Cup will be held in the United States, Mexico and Canada from June 11th to July 19th.
"Our children are not safe and, fundamentally, such conditions for participation do not exist," Donyamali said.
"Given the malicious actions they have carried out against Iran, they have forced two wars on us over eight or nine months and have killed and martyred thousands of our people. Therefore, we certainly cannot have such a presence."
In the draw last December, the Iranians were grouped with Belgium, Egypt and New Zealand. All three of their Group G matches were scheduled to take place in the US, two in Los Angeles and one in Seattle.
Iran was the only nation missing from a FIFA planning summit for World Cup participants held last week in Atlanta.
Reuters has contacted FIFA for comment.