MP Damian Collins has asked the body to investigate whether the payment breached bribery laws.
The £3.9m payment was made to the FIA for entering into an agreement with the teams and sport's commercial arm.
The FIA says the payment was remuneration "for its regulatory role" and denies wrongdoing.
Collins, chairman of the Culture, Media and Sport Parliamentary select committee, said he was "very concerned" about why the sport would need to make a payment to its governing body and regulator as part of the so-called Concorde Agreement, which was signed in 2013.
"That's why I've written to the Serious Fraud Office (SFO) asking them 'do they feel there was a breach of the Bribery Act and does it warrant investigation'?" he told ITV.
An SFO spokesperson told BBC Sport: "The Serious Fraud Office is reviewing material in its possession in relation to these allegations. All matters referred to the SFO are assessed against criteria to establish whether they may fall within its remit to investigate."
The FIA confirmed in a statement that it had received the payment and explained: "The Concorde Implementation Agreement entered into by the commercial rights holder of Formula 1 and the FIA in 2013 introduced a new governance structure for Formula 1 and redefined certain conditions applicable to their relationship, in particular to ensure that the FIA be properly remunerated for its regulatory role.
"Within this agreement, a lump sum payment of $5m (£3.9m) was made to the FIA as part of the global consideration received in connection with the renegotiation of the terms of the agreements between the commercial rights holder and the FIA, and of the Concorde Agreement, at that time.
"Following its approval, the Concorde Implementation Agreement came into force and this sum was paid to the FIA and properly accounted for.  No individual received any payment out of this sum. Any allegation to the contrary would be defamatory."
The Serious Fraud Office is "reviewing material" relating to a payment made by Formula 1's commercial rights holder to the sport's governing body the FIA.