Officers from the Carabinieri military police swooped in the early hours to arrest people on a range of charges that include a criminal conspiracy to corrupt public officials.
Nobody from Roma has been arrested or charged by police.
Italian media reported that among those taken into custody is Luca Parnasi, owner of the construction company Eurnova, which is in line to build the new ground.
Also arrested was Adriano Palozzi, vice-president of the Lazio region where Rome is located, regional councillor Michele Civita and Luca Lanzalone, the head of municipal electricity company ACEA, who has worked closely with Rome mayor Virginia Raggi in the ongoing approval process.
"Those who did wrong will pay. We're for legality. if everything is up to standard then we hope that the project can go ahead," Raggi said.
Raggi was fiercely against the building of the new stadium in the Tor Di Valle district in south-western Rome before being elected mayor in 2016.
However, on Tuesday she said on Twitter that her council was working to shorten the time it will take to approve the 52,500-capacity ground and connected business park.
Roma, who last season finished third in Serie A and reached the semi-finals of the Champions League for the first time in more than three decades, have been hoping to start construction by year end.
The project, set to cost in the region of €800 million, has been crawling through Italy's notorious bureaucracy since its initial unveiling by club president, billionaire US businessman James Pallotta, in March 2014.