Mauro Contini the mayor of Quartu Sant'Elena, the Cagliari district where the stadium is located, was also arrested along with another local official by the Forestry corps, an agency of the Italian police, the source said.
They were charged with embezzlement and false representation in the rebuilding of the stadium.
"Officers, employees, technical staff and players are close to their president Massimo Cellino in these difficult times," said the statement.
"We have faith in the work of the judiciary and are confident that the investigation will show the non-involvement of president in the alleged facts.
"At this time we would like to say just one thing: "Strength to the president, we are with you."
On that occasion, Cellino told fans the ground was safe, invited them to turn up for the match anyway and slammed the city government for placing bureaucratic obstacles in the club's way.
Last Sunday's game against AC Milan was initially set to be moved to Turin amid security worries but eventually went ahead at the stadium after a regional tribunal ruled it was safe.
Cagliari had played at the Stadio Sant'Elia from 1970 until around halfway through last season but abandoned the arena due to disagreements with the local authorities and over growing safety worries.
