Israeli police and domestic intelligence said the man was twice smuggled into Iran and received payment to carry out missions.
In a joint statement, they said the suspect was a businessman who had lived in Turkey and had Turkish contacts who had helped get him into Iran.
The announcement comes at a time of soaring tension between Iran and Israel, regional arch-enemies.
The statement said the suspect, who was not identified, was arrested last month. It said his targets were the prime minister, the defence minister and the head of Israel internal security agency Shin Bet.
It said that in April and May, the suspect twice travelled to Samandag in Turkey to meet a wealthy Iranian businessman called Eddie, and was helped by two Turkish citizens.
The statement said Eddie had problems leaving Iran on both occasions, so the Israeli citizen was smuggled from Turkey into Iran instead. It said that the man met both Eddie and an Iranian security operative there.
It said Eddie asked the Israeli to carry out various security missions within Israel for the Iranian regime.