The attack occurred today in Thessaloniki, Greece's second largest city, and police said they have no information about a possible motive for the attack.
The slain parents, aged 54 and 42, and their son were not immediately identified.
Police say the suspected attacker, a 60-year-old man, was hospitalised under police guard and has been formally arrested.
He appeared to have suffered a stab wound, believed to be self-inflicted.