The investigation began after a whistleblower raised concerns over the treatment of residents at Colinton Care Home, which houses 53 elderly residents.
Bosses at Four Seasons Health Care (FSHC), which runs six homes across the Capital, including Colinton through subsidiary firm Brighterkind, said they were helping the police investigation and that relatives had been informed.
They also stressed that it was one of their own carers who had reported the alleged incidents and that the home has an “active whistleblowing policy”.
In a statement, FSHC said: “When one of our care staff raised concerns about the conduct of colleagues the home manager notified all the relevant authorities and we have been cooperating actively with a police investigation. Three members of staff have been suspended pending its outcome. We have informed relatives of people living in the home.
“The wellbeing of the people in our care is our priority and we have an active whistle-blowing policy that encourages our residents, relatives and staff to raise any concerns they may have and these are always followed up and referred to relevant authorities as appropriate so that they may be investigated in a thorough and transparent way.
“We are grateful to our carer for their vigilance in raising concerns that have led to the investigation.
“It is not appropriate to comment further ahead of the conclusion of the investigation and any subsequent legal process.”
Police Scotland confirmed they had received a complaint relating to a care home in the south side of Edinburgh, and said their inquiries were ongoing.
A council spokeswoman said the authority was aware of the concerns raised and was working with its partners to address them.
The police and the home have been unable to confirm how long the investigation will take or any details of the allegations. None of the three carers, who have not been named, have yet been charged with an offence.
Four Season Health Care runs 350 care homes across the UK, including Guthrie House in Liberton, Merchiston, Castlegreen in Niddrie, St Margaret’s in Newington, and Gilmerton.
A FSHC spokesman stressed that each home had its own “separate management team and staff”.
A Colinton Care Home nurse was jailed for 15 months in May 2007 for tormenting dementia sufferers.
Jeffrey Ednalan, 34, was convicted of a catalogue of abuse including stuffing a deodorant can in the mouth of a 95-year-old man to stop him shouting and two counts of indecent assault.
The Filipino handled an 86-year-old woman’s naked breasts and also left seven residents in soiled incontinence pads all day to “save time”.
Ednalan denied all of the charges at Edinburgh Sheriff Court and insisted his fellow workers at the Colinton Care Home had made up the allegations out of jealousy.