Cellino, 56, was taken to the Buoncammino prison along with Mauro Contini, the mayor of Quartu Sant'Elena, where the stadium is based, and public works commissioner Stefano Lilliu.
Reports in Italy suggest the Guardia Forestale are investigating alleged attempted embezzlement and fraudulent misrepresentation surrounding the unfinished stadium, where Cagliari have struggled to host home games throughout the season.
Cellino has argued the new build - which has a potential capacity of 16,200 - meets safety requirements but persistent concerns have arisen concerning the appropriate use of invested funds and the length of time being taken to complete the stadium.
Cagliari later published a statement in support of Cellino, who took control of the club in 1992, on their official website.
It read: "All the directors, employees, coaches and players are close to their president Massimo Cellino at this difficult time.
"We are confident in the work of the judiciary and we are confident the investigation will show how the president is not connected to the facts alleged against him.
"No one can testify to the fairness, honesty and competence of Massimo Cellino. At the moment we want to say this - come on president, we are with you."
Contini, meanwhile, complained of feeling ill during questioning and was transported by ambulance to the nearby Brotzu hospital for medical tests, where he remains.
Deputy mayor Fortunato Di Cesare told Unione Sarda: "The administration will continue to work towards maintaining clarity despite our deep emotional involvement in these events.
"In situations like this the public must be protected. For that reason we will do everything we can to ensure that the administration of policy does not slow down.
"We hope that all the members of the city's council will show solidarity at this difficult time and contribute loyally to running the city's administration.
"Any further investigation into this matter, which is yet to be thoroughly evaluated by the authorities, should not be used for personal or political purposes."
Today's high-profile arrests follow those of November when entrepreneur Antonio Grussu and councillors Pierpaolo Gessa and Andrea Masala were questioned about the construction of the Is Arenas.
Cagliari left their previous Stadio Sant'Elia base during the final weeks of the 2011-12 season and played their remaining home games over 650 miles away at the Stadio Nereo Rocco in Trieste.
Atalanta played behind closed doors in Cagliari's first home game of the current season but Roma were awarded a 3-0 walkover victory in September when Cellino defied orders to forbid fans from attending the next home game, with a match against Juventus being moved to Parma's Stadio Ennio Tardini in December.
The Lega Serie A ordered Cagliari to host AC Milan at the Stadio Olimpico in Turin on Sunday but the Sardinian club successfully appealed against the decision.