Wayne Rooney senior, 48, was detained at his home in the West Derby area of Liverpool.
The arrests, carried out across Merseyside and Glasgow, relate to a game between Motherwell and Hearts in December last year, which Hearts won 2-1 following a second half penalty.
The Motherwell midfielder Steve Jennings was arrested after allegedly getting himself sent off deliberately during the match.
It is believed that there was a pattern of irregular betting, with stakes being put on a red card being given. One was allegedly from a new account opened in Liverpool, from where £500 was staked at odds of 10/1.
Rooney's 48-year-old father, also called Wayne, is thought to have been arrested at his home in the West Derby district of Liverpool.
The investigation relates to a match between Motherwell and Hearts on December 14 last year, Merseyside Police said.
It is also understood that Manchester United star Rooney's uncle Richie, 54, was also detained.
All the suspects are being held for questioning at police stations across Merseyside.
In a statement, Scottish Football Association chief executive Stewart Regan said the arrests follow "extensive inquiries" into alleged betting irregularities at the Scottish Premier League match.
Regan said: "While the investigation involves several other individuals out with Scotland, it is important to stress that the evidence gathered throughout this thorough period of investigation has involved only one Scottish match.
"Motherwell FC are aware of the situation and will issue a response in due course.
"The Scottish FA will make no further comment at this stage."