Al-Ittihad's Morocco international Hamdallah was whipped by a fan in scenes that have gone around the world.
A joint statement from the SAFF and PFA declared: "Football in Saudi Arabia is a family sport, and fortunately, spectator unrest is extremely rare.
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"Therefore, the actions of this 'so-called' fan go against everything that Saudi football represents and we completely condemn the episode.
"A thorough review of the spectator conduct rules will be carried out. The review will ensure that updated rules and regulations are introduced to quickly and effectively impose appropriate penalties and to avoid the recurrence of such episodes."