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 37-year-old, who set a new lap record of 134.089mph at the Ulster Grand Prix in August, will also race in the British Superstock 1000cc series.
The Bingley rider won Superstock races at the North West 200, TT and Ulster GP this year.
He was also a double winner in the Superbike class at Dundrod on his BMW.
The Yorkshireman finished second in this season's British Superstock 1000cc series.
Hutchinson is also set to continue to compete in the Supersport class, in which he has enjoyed substantial success with Keith Flint's Team Traction Control Yamaha outfit in recent years.
A hat-trick hero at this year's TT and a four-time winner at this year's Ulster Grand Prix, Hutchinson has set his sights on further improvement next year.
He finished second to Michael Dunlop in both the Superbike and Senior TTs in 2016,
"Having now worked together for a season, we know where we need to improve with the obvious goal, to go on now and challenge for the Superbike wins at all of the big three internationals," said Hutchinson.
"The BMW S1000RR still has so much potential in Superbike trim on the roads and with another season of British Superstock planned, the aim there will be to go one step better and win the championship next season."
"Hutchy did a great job for us this season and whether it was in British championship or the roads, he was always in contentions for wins and podiums and provided both our sponsors and fans with a lot of entertainment," added team owner Hector Neill.
"His international hat-trick in the Superstock class and his terrific season in British Superstock proved how well he got on with the Tyco BMW, and to go on and take the world's fastest track lap record at Dundrod was the icing on the cake.
"The goal going forward is to build on that success and I've never hidden the fact that the Senior TT trophy is the one we really want to win in 2017.
It's the blue-riband road race on the season's calendar, and along with Hutchy and our dedicated team we will be giving it our very best shot."
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.
[NEXT_CONCEPT]
Fourteen-time Isle of Man TT winner Ian Hutchinson is to stay with the Northern Ireland-based Tyco BMW team for the 2017 international road racing season.