Interactive Telephone Services - whose group chairman is the former Conservative minister, Tim Renton - said the game, Telemillion, was being temporarily suspended until a dispute about its legality was clarified.
The decision follows investigations by Hampshire Police to decide whether Telemillion was a game of chance, and, therefore, an illegal lottery, or a contest of skill.
To play the game, launched in January, competitors ring an 0891 premium charge number and answer a question correctly, after which their names go into a prize draw.
ITS, based in Southampton, Hampshire, said it was confident that the police would conclude the game was legal.
'Our solicitors have written to Hampshire Police urging them to conclude their inquiries quickly, as we believe there is no case to answer,' Michael Biden, its chief executive, said. 'There have been doubts about the degree of skill required, as well as the free entry route, but the questions asked in the Telemillion game are far harder than most other competitions.'
He added: 'We have come to the view that, while there is a legal debate about this, the game should be suspended.'
Mr Biden said that millions of people had played the game since its launch and there were more than 14,000 cash prize- winners, including three jackpot winners. Steven Hart, 34, a builder from Rawmarsh, South Yorkshire, won the pounds 250,000 April jackpot.
Mr Renton, a former arts minister and chief whip - and ITS group chairman since July - was at the directors' meeting which decided to suspend the game.
A Hampshire Police spokeswoman said that inquiries into whether the game was in breach of lotteries legislation were at an early stage.