Spanish Women coach, Luis Rubiales kissed forward Jenni Hermoso on the lips after Spain beat England.
He earlier grabbed his crotch as he celebrated at the final whistle.
According to reports in Spain Rubiales is set to announce his resignation on Friday and has already informed colleagues of his decision.
Fifa will look at whether his actions constitute violations of article 13 in its disciplinary code, concerning offensive behaviour and fair play.
"Fifa reiterates its unwavering commitment to respecting the integrity of all individuals and strongly condemns any behaviour to the contrary," it said in a statement.
According to the disciplinary code, officials are among those that must "comply with the principles of fair play, loyalty and integrity".
It says disciplinary measures can be brought against anyone "violating the basic rules of decent conduct", "insulting a natural or legal person in any way, especially by using offensive gestures, signs or language" or "behaving in a way that brings the sport of football and/or Fifa into disrepute".
Luis Rubiales' celebration at the final whistle was in the VIP area of Stadium Australia, while he was standing near Queen Letizia of Spain and her 16-year-old daughter.
He then kissed Hermoso on the lips after she was presented with her winner's medal on the podium.
Rubiales apologised for the kiss on Monday, but Spain's Prime Minister Pedro Sanchez said that was "not enough" and second deputy prime minister Yolanda Diaz joined those calling for him to resign.
Futpro, a union representing Hermoso, said the incident should not go unpunished, and the 33-year-old said the union would "defend my interests" in the matter.
The Pachuca player, who has earned 101 caps, had initially said on Instagram she "didn't like" Luis Rubiales' actions but a statement released later on her behalf defended him.
The Spanish football federation (RFEF) has called an extraordinary general assembly to be held on Friday "as a matter of urgency".