The men, both of whom suffer from dementia, came to blows a week ago Saturday night, a time when most residents at the facility watch the Melodifestivalen song contest on television.
At the time the fisticuffs broke out, staff members were in another wing of the facility. The 90-year-old had been hit and kicked and was later taken to hospital, where he died last Thursday.
The incident has been reported to both the police and the National Board of Health and Welfare (Socialstyrelsen), according to Sveriges Radio (SR).
"It's a real tragedy. Not only for the resident who died and those close to him, but also for the resident and those close to him who was involved in this," said Annelise Håkansson, head of care facility administration in Lund, to SR.
According to SR, the men had only lived at the facility for about a month, but in that short time span had managed to get into several altercations.
They were nevertheless allowed to continue living near one another.
Officials from Lund municipality, which is responsible for the care centre's management, estimate that the wing where the fight took place was unstaffed for about 20 minutes around the time the two men began fighting.
It remains unclear if the 90-year-old died of injuries sustain in the fight.