The 33-year-old arrestee was injured while grabbing onto a toilet at Colchester police station on 1 May.
The Independent Police Complaints Commission (IPCC) said all six officers face allegations of assault and using excessive force.
Essex Police said one officer had been placed on restricted duties.
It declined to comment further due to the investigation. The IPCC said the allegations could amount to gross misconduct if proven.
The man was taken into custody on 30 April in relation to a public order incident, but in the early hours of the next day a number of officers entered his cell to find him standing with one foot in the metal toilet bowl.
The IPCC said he held on to the rim on the bowl while the officers tried to restrain him.
Soon after, according to the watchdog, the tops of three of the man's fingers on his left hand were severed.
The tops of the fingers were later recovered from inside the toilet and transported to the hospital, but it is believed they were not reattached successfully.
The IPCC said it would look at whether the officers' restraint was "appropriate" and caused the man's injuries.
Investigators will consider whether the man's mental health or ethnicity influenced the actions of officers.
Additionally, they will examine why there was a delay of around five hours in retrieving and transporting the severed fingertips to hospital.
Six police officers are being "criminally investigated" after a man lost the tips of three fingers during a struggle in his cell.