The IFF accepted Mayelikohan's resignation, which was handed in earlier on Tuesday, according to a short statement published on the federation's official website.
The resignation comes only two weeks after Mayelikohan took the post following Ali Daei's dismissal.
However, his recent remarks against Esteqlal coach Amir Qalenoi sparked widespread criticism from the media.
Mayelikohan, who is also the manager of Iranian Premier League side Saipa, claimed that Qalenoi had incited a group of Esteqlal's fans to chant insulting slogans against him during the two teams' match on Friday.
The IFF head Ali Kafashian said a new coach would be selected for the national team in the next few days from the candidates which had been considered for the post before Mayelikohan's appointment.
Former Persepolis manager Afshin Qotbi, Esteqlal's Amir Qalenoi, Fajr Sepasi boss Qolam Hossein Peyrovani and Rah Ahan's Mahmoud Yavari were among the candidates considered for coaching the national team.
Iran, which is in Group B of the 2010 World Cup qualifiers along with Saudi Arabia, South Korea, the UAE and North Korea, will meet North Korea in its next match on June 6.
South Korea tops the group with 11 points, one point ahead of North Korea and Saudi Arabia. Iran is placed fourth with six points, while the UAE is at the bottom of the group with only one point.