The players were banned for 12 months after FIFA found that false documentation had been used so they could play in an Asian Cup qualifier for Malaysia against Vietnam.
All seven players appeared in Malaysia's 4-0 win over Vietnam in the third round of the 2027 Asian Cup qualifiers in June.
"The (FIFA Appeal) Committee instructs the Secretariat to take immediate steps to launch a formal investigation into the internal operations of the FAM," FIFA said.
"This investigation shall aim to identify the individuals responsible for the falsification of documents, assess the adequacy and effectiveness of FAM's internal compliance and governance mechanisms, and determine whether additional disciplinary measures are warranted against FAM officials."
FIFA's findings sparked uproar, with fans and lawmakers calling for action against FAM as well as the national registration department and home ministry.
Last month, the FAM suspended its secretary-general and formed an independent committee to investigate.
FIFA also ordered the FAM to pay a fine of 350,000 Swiss francs ($439,000) and this month the sport's ruling body dismissed its appeals.
The report showed how Facundo Garces, Gabriel Arrocha, Rodrigo Holgado, Imanol Machuca, Joao Figueiredo, Jon Irazabal and Hector Hevel - all born outside Malaysia - were granted Malaysian nationality in a process supervised by the FAM.
The players claimed their grandparents were born in Malaysia, but FIFA was able to obtain birth certificates that had significant discrepancies with those submitted by FAM to show the players' Malaysian lineage.
"Players admitted at the hearing that they did not read any of the application documents submitted to the Malaysian government, including the part which concerned the declaration that they had lived for 10 years in Malaysia," FIFA said.
"The players explained that following the submission of documents, FAM undertook the bureaucratic steps necessary for the players' naturalization."
FIFA described how one player, Arrocha, claimed: "My grandfather was born in Venezuela and my grandmother in Spain... I mean Malaysia, sorry," while expressing confusion about discrepancies in birth certificates.
FIFA also directed the Secretariat to notify criminal authorities in Brazil, Argentina, the Netherlands, Spain and Malaysia.
"It is imperative that the relevant authorities are informed so that appropriate criminal investigations and proceedings may be pursued," FIFA said.