Interpol has put out a "red notice" for Mr Vahidi
The US has said Iran is "taking a step backward" by appointing a cabinet minister suspected of terrorism.
President Mahmoud Ahmadinejad chose Ahmad Vahidi, wanted by Argentina over the deadly 1994 bombing of a Jewish centre, as his new defence minister.
Mr Vahidi was strongly supported by Iran's parliament, the Majlis, with 227 MPs backing him out of 286, Iranian Speaker Ali Larijani said.
The US State Department described the appointment as "disturbing".
"Iran today is taking a step backward by putting into a high office a well-known individual suspected of participation in a terrorist act," said state department official PJ Crowley.
Defence: Ahmad Vahidi - his appointment is controversial internationally because Argentina wants his arrest over a 1994 attack on a Jewish centre
Interior: Mostafa Mohammad Najjar - a senior figure in the elite Revolutionary Guards; critics ask whether a military commander should run interior affairs
Health: Marzieh Vahid Dastjerdi - first woman cabinet minister since 1979; seen as inexperienced
Oil: Massoud Mirkazemi - currently commerce minister, has close links to the Revolutionary Guard; his knowledge of the oil industry has been questioned
Intelligence: Heydar Moslehi - a former representative of Iran's Supreme Leader in the Basij militia; critics say he has never worked in intelligence
"For Iran, it is sending precisely the wrong message."
US President Barack Obama has given Iran until later in September to agree to new talks on its nuclear programme, or face tougher sanctions.
The US said it had hoped that Iran would take "a step forward to engage" with the world, showing "a new approach".
Taking up his post, Mr Vahidi was quoted by Reuters news agency as saying: "All those who act against Iran will face the iron fist of the Iranian government, nation and armed forces."
Interpol has distributed Argentina's warrant for Mr Vahidi's arrest over the attack at the Israeli-Argentine Mutual Association (AMIA) of Buenos Aires in 1994, which killed 85 people.
The US supported Argentina's efforts to prosecute those responsible for the bombing.
At the time of the attack Mr Vahidi was the commander of a special unit of Iran's Revolutionary Guard known as the Quds Force.
Israel and Argentina had earlier condemned Mr Vahidi's nomination, with Buenos Aires calling it "an affront to the victims" of the bombing.
The state prosecutor who investigated the bombing, Alberto Nisman, described Mr Vahidi's appointment as a clear signal of defiance, and said Iran had always refused to co-operate with Argentina's courts.
Iran has denied any involvement in the blast and says the case against it is politically-motivated.