Iran's semi-official Fars news agency said Mr Rajaei "took a picture with and hugged" his Israeli counterpart.
State news agency Irna said the Iranian contestant held his national flag next to the Israeli flag.
A picture of the two men circulated on Iranian state media outlets.
Mr Rajaei was banned for "crossing the red lines of the Islamic republic", agencies reported. The weightlifting federation also dismissed the head of Iran's delegation Hamid Salehinia.
Iran does not recognise Israel, which it calls an "enemy" and prohibits all contact between Iranian and Israeli athletes.
Mr Rajaei is a former member of the Iranian national team and represented his country at the Asian Weightlifting Championships in Thailand in 2015.
In 2021, Iran's supreme leader Ayatollah Ali Khamenei urged athletes "not to shake hands with a representative of the (Israeli) criminal regime to obtain a medal".
For years, Iranian athletes have managed to avoid meeting Israelis in competitions, often by getting disqualified or providing medical certificates testifying that they were unwell.
Young chess prodigy Alireza Firouzja left Iran after the sport's federation banned him from playing in the 2019 world championship for fear he would face an Israeli player. He is now a naturalised French citizen.