Valentin Balakhnichev is the only person to serve as president of the federation since it split from the Soviet track and field authorities.
He departs with the federation facing a World Anti-Doping Agency investigation into allegations of systematic and organized drug use by Russian athletes.
The biggest focus is on Russia's world-beating race-walking team, which has seen more than 20 athletes banned for doping.
Three Russian Olympic walking champions were banned for doping last month and the Russian anti-doping agency says their blood samples show similarities indicating an organized program of drug use.
Speaking at a national championship competition, Balakhnichev said "the president takes full responsibility and so I decided to resign," in comments reported by the R-Sport agency.
Vice-President Vadim Zelichenok will serve as acting president until elections are held, federation spokesperson Alla Glushchenko told The Associated Press.
That will be no later than six months after next year's Olympics, R-Sport reported.
In almost his last act in office, Balakhnichev announced that a scandal-hit athletics coach had been reappointed to a senior position less than a month after he resigned amid several doping scandals.
Valentin Maslakov served as head coach of the Russian national team from 2007 until last month, when he stepped down shortly after the three Olympic champion race-walkers were banned.
Maslakov will now serve as senior sprinting coach, a position one rank below his old job, Balakhnichev said.Suggest a correction