The attacks killed the Islamic Republic's Supreme Leader Ayatollah Ali Khamenei and triggered a region-wide conflict.
"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 48-team World Cup will be held in the U.S., Mexico and Canada from June 11 to July 19.
"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."
More than 1,300 Iranian civilians have been killed since the US and Israeli airstrikes began on February 28, according to Iran's U.N. ambassador Amir Saeid Iravani.
Iran drawn to play in LA and Seattle
Iran are grouped with Belgium, Egypt and New Zealand.
All three of their Group G matches are scheduled to take place in the U.S., two in Los Angeles and one in Seattle.
Iran, who dominated the Asian qualifying rounds to qualify for the tournament in March last year, was the only nation missing from a FIFA planning summit for World Cup participants held last week in Atlanta.
There was no immediate comment from the Iranian Football Federation or world soccer's governing body FIFA.
FIFA regulations state that any team that withdraws from the tournament "no later than 30 days before the first match" will be fined at least 250,000 Swiss francs ($320,800).
"Disciplinary sanctions may include the expulsion of the participating member association concerned from subsequent FIFA competitions and/or the replacement of the participating member association with another member association," FIFA's regulations say.
"The FIFA Council or the relevant committee may decide, in particular, to replace the member association in question with another association."
Iran had selected Tucson's sprawling Kino Sports Complex as the team's base camp and 18 months of preparation hang in the balance with a potential economic hit in Arizona.
There is also the question of tickets to World Cup games involving Iran. Should Iran boycott the tournament, Iranian fans who bought tickets for eye-watering prices may be tempted to sell them on the huge resale market.
Infantino says Trump welcomes Iran team
Earlier, FIFA President Gianni Infantino said he had met US President Donald Trump, who told him he welcomed Iran's participation in the World Cup.
Trump had previously said "I really don't care" if Iran participated or not, but Infantino said he had a productive discussion with the president.
"During the discussions, President Trump reiterated that the Iranian team is, of course, welcome to compete in the tournament in the United States," Infantino said.
A source in Tehran familiar with the matter said that, as well as Iran's decision not to attend the World Cup, warm-up games were not possible because of the war.
Earlier this week, Australia granted humanitarian visas to five Iranian women soccer players after they sought asylum, fearing persecution on their return home for their refusal to sing the national anthem at a Women's Asian Cup match.
Trump had called on Australia to give asylum to members of the Iran women's soccer team.
On Wednesday, Australian police helped two more members of the Iranian women's soccer delegation slip their minders to claim asylum, but one has changed her mind and decided to go back to Iran, the country's interior minister said.