Mr Ross, 37, took up the post of leader of the Scottish Conservatives in August, and is also a part-time professional football referee.
But as first reported in The National, images featured on leaflets inviting the public to 'meet Douglas Ross' showed the Moray MP as a professional referee, wearing a shirt emblazoned with the FIFA badge.
The pamphlets were sent to homes around Scotland. The image of Mr Ross was also used by the party for their campaign calling on the Scottish Government to create a "fans fighting fund".
But FIFA has been contacted by an irked football fan who believes an investigation should be launched.
If found guilty of breaking the world football governing body's statutes, Mr Ross could face a ban from the sport.
FIFA's rules state they do not take a position "in matters of politics and religion".
On Sunday a member of the Scottish Football Supporters Association wrote to FIFA suggesting Mr Ross's use of the logo questions "the integrity of football".
The fan, who wished to remain anonymous, wrote: "I want FIFA to launch an investigation and deal with this matter as a matter of urgency, given that we are now in an election cycle in our country.
"This leaflet has been distributed by the political party that Mr Ross leads.
"It has been sent to households throughout Scotland and it clearly shows him using his image as a FIFA official to try and benefit himself and his organisation with this endorsement."
Keith Brown, the SNP's depute leader, said: "In his desperation for attention Douglas Ross has irked an awful lot of people.
"FIFA are absolutely right to have launched an investigation on the Scottish Tory boss.
"Many people think he should be sanctioned for politicising the beautiful game this way.
"In May - at the most important election Scotland has ever had - voters have the opportunity to give Ross and Boris Johnson the red and vote to put Scotland's future in Scotland's hands by voting SNP."
In 1995 Swiss referee Kurt Rothlisberger was suspended for three months for giving unauthorised publicity to a political party.
Mr Rothlisberger, who was campaigning for a seat in the Swiss National, was photographed in his official FIFA referee uniform, displaying the logo of his political party next to the FIFA emblem.
A FIFA spokesman said: "We are currently looking into the matter and have no further comment to make at this stage."
A Scottish Tory spokesman said: "Douglas will be happy to clarify matters with FIFA and is not aware of any concerns from the association."
The probe comes as Mr Ross yesterday criticised his own party’s approach and accused them of alienating the Remain voters of Scotland.
Delivering the keynote speech at Policy Exchange yesterday morning, Mr Ross also demanded more was done to show the “shared values” of the UK.