Segura, who had been in charge since Julio Grondona's death, had been at the AFA headquarters on Monday but left shortly before midday following a bomb threat at the building.
AFA sources confirmed to Clarin that the president subsequently handed in a letter of resignation to authorities and "will not return" to Viamonte before his term ends on June 30.
The ex-Argentinos Juniors chief's resignation comes in the wake of further turmoil for the troubled AFA, after being threatened with possible suspension from FIFA should they not accept overseers in the institution.
Segura's exit would clear the way for Damian Dupuilliet to take over as an interim president and for a FIFA normalisation committee to oversee matters, despite a ruling from Judge Maria Servini de Cubria ordering the world governing body to be blocked from the institution.
Intervention from judicial authorities in May blocked elections that had been scheduled for June 30, meaning the AFA is set to continue in limbo without Segura at the helm.