Retired company director Philip Rutherford, who served in the Royal Navy in the Second World War, is said to have been hit on the head and body during the incident at Edinburgh's Western General.
The incident, which left the pensioner with a broken hand and lacerations to his face, took place during the night.
Mr Rutherford's family were telephoned and told the pensioner had been involved in an incident.
Mr Rutherford's son-in-law Colin Kelly, 61, said: "My father-in-law is very frail. "The hospital phoned and said he had been in a scuffle and had a small injury, but when we saw him we thought, 'this is a bit more than a small injury'.
"Philip had a bleeding in the skull a few years ago that had been caused by a head injury and we are extremely worried there could be a recurrence because of this.
"The charge nurse said it was a wee shame and at this point I was incandescent with rage. When we asked the hospital staff if police had been contacted we were told they hadn't.
"They claimed my father-in-law – who was dazed at the time – said he didn't want the police involved, but I insisted they were. It was a shock and a trauma for us all, but most of all for Philip."
Mr Rutherford, who lives in retirement flats in Leith, is the former director of an antiques business. He had been in hospital for two weeks suffering from a recurring illness.
Mr Rutherford is still in the hospital receiving treatment.
Dr David Farquharson, NHS Lothian's medical director, said: "I can confirm a patient suffered injuries following an incident in the Western General Hospital.
"We took the matter very seriously indeed, assessed the patient, provided appropriate treatment and reported it to the police.
"We have a duty of care to all our patients and have ensured all relatives were informed. An investigation is under way."
A Lothian and Borders Police spokesman said a 58-year-old man had been arrested and reported to procurator-fiscal following an alleged assault within the Western General Hospital. The spokesman added: "A man aged 87 suffered injuries to his face and hand during the incident."
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