Cantonal police discovered the woman dead in her house in the city of Aarau on Wednesday after the victim’s daughter sought help after getting no response when she visited the elderly woman.
Police on Thursday said they had arrested the son, who used to live with his grandmother before moving to an apartment.
It is not clear what the motive for the killing was and the exact circumstances of the death had yet to be clarified, police said.
The man was described by daily newspaper Blick online as a loner who practised serves by himself at the local tennis club.
“He has mental problems,” his father told the newspaper, while acknowledging he had not seen him for three years.
The man’s father and mother divorced 17 years ago and the son lived with his mother, Blick said.
Neighbours noticed that the grandmother’s car had remained parked since Christmas, 20 Minuten newspaper reported online.
Neither the grandson, who appeared to have no job and previously visited his grandmother frequently, nor the victim had been seen outside the house for a long time, the daily said.
Elsewhere in the country, police in Basel have arrested two men, aged 28 and 26, after discovering a dead person in an apartment.
The victim, who died several days or possibly weeks ago in the home of one of the suspects, has yet to be identified, the city’s prosecutors office said.
The person had been reported missing for several days.
Police initially arrested a 26-year-old man who lives in the apartment.
On Thursday officers picked up a 28-year-old man, who was also believed to be in the apartment at the time of the victim’s death.
The two suspects are Swiss citizens described as being involved with the illegal drug trade.