A Formula One spokesman said content belonging to regional rights-holder, Qatar-based beIN Sports, had been transmitted by beoutQ.
"Formula One takes intellectual property infringement of this nature extremely seriously, we are looking into the issue and those that are involved and will take appropriate action," Formula One said in a statement at the French Grand Prix.
European soccer body UEFA has threatened action over beoutQ's airing on Riyadh-based satellite provider Arabsat of the World Cup in Russia, as well as the Champions and Europa Leagues.
Arabsat was founded in 1976 by Arab League member states.
UEFA alleges beoutQ is illegally using content from beIN Sports, which holds the regional rights but is blocked in Saudi Arabia under a boycott of Qatar by Riyadh and Arab allies.
Saudi Arabia, the UAE, Bahrain and Egypt imposed a boycott on Qatar in June 2017, accusing it of supporting terrorism, which Qatar denies.
Formula One did not mention Saudi Arabia in its statement.
Saudi Arabia's media ministry on Friday denied that beoutQ was based in the kingdom and said authorities were working to prevent beoutQ's activities in Saudi Arabia. It said beoutQ's set-top boxes were widely available in other countries, including Qatar and eastern Europe.
BeoutQ could not be reached for comment. It is unclear who owns and operates the channel.
World soccer body FIFA has also accused beoutQ of illegally broadcasting the opening games of the World Cup.
Saud al-Qahtani, a senior adviser to Saudi Crown Prince Mohammed bin Salman, has called the piracy charges "baseless" and "unfounded", accusing Qatar of trying to divert attention from the dispute with its neighbours.
The Middle East has two Formula One races, in Abu Dhabi and Bahrain.
The region is also a major market for luxury car manufacturers like Mercedes and Ferrari.
Formula One's commercial rights are owned by U.S. company Liberty Media.
(Reporting by Alan Baldwin, editing by Ian Chadband and Nick Tattersall)
