The missing men - all from Naples - were last seen on 31 January in Tecalitlán, in the western state of Jalisco.
The state's governor said the officers had confessed to handing the Italians over to a local criminal gang.
The police had allegedly arrested them at a petrol station beforehand.
What is alleged to have happened?
Raffaele Russo, 60, his 25-year-old son Antonio, and his nephew, Vincenzo Cimmino, 29, had stopped at a petrol station in Tecalitlán, an agricultural town.
The last relatives back in Italy heard from them was a Whatsapp message from Mr Russo saying they had been approached by police officers who arrived on cycles and in a van.
The police told them to follow them, according to the message.
The son of one of the disappeared earlier told Italian radio that the men had been "sold to a gang for €43" ($53; £38), but regional officials said they could not confirm that information.
The area is controlled by the Jalisco New Generation cartel, one of Mexico's most powerful criminal gangs.
Four police, including a female officer, have been detained and charged. The Mexican authorities say three more police are being sought in connection with the disappearance.
Following the trio's disappearance, the town's entire police force was sent for retraining, although some local media speculated that they were sent away so that they could not be intimidated by local cartel members into changing their story.
What were the Italians doing in Mexico?
It is not absolutely clear, but reports say they were there to sell Chinese merchandise.
Jalisco State Prosecutor Raúl Sánchez said he had information showing the three were selling cheap generators and agricultural machinery which they passed off as high-quality branded goods.
Relatives in their home town denied the three were doing anything illegal in Mexico.