He had been appointed in August after authorities dissolved Kuwait's FA amid a clampdown on sports governing bodies.
Hassawi had been appointed in August after authorities dissolved Kuwait's Football Association amid a clampdown on sports governing bodies that triggered strong international criticism.
Hassawi announced his resignation on Twitter late Sunday without giving a reason.
But his decision came only hours after the competitions committee at KFA rejected complaints by two league teams over allowing two sides to field suspended players.
"Justice and equal opportunities do not exist in your federation," wrote Al-Arabi club on its Twitter account addressing Hassawi. "Your presence in the temporary committee tarnishes your sportive history."
Al-Arabi and Al-Salmiyah clubs had complained following their respective league matches with Al-Kuwait and Al-Jahra. But the competitions committee insisted that the concerned players were suspended in the Crown Prince Cup competition, not the league.
Al-Arabi has since withdrawn from the league.
Kuwait's sports authority have come under strong international criticism over its clampdown on sporting bodies.
Authorities in August sent in police to take over Kuwait's Olympic Committee and the KFA.
Last month, world football governing body FIFA joined the International Olympic Committee in threatening legal action against Kuwait over the government takeover of sporting bodies.
The IOC and FIFA suspended Kuwait in October last year over government interference in sport. It is the second time in five years the Gulf state has been suspended.