The emergency services were called to Poddle Park in Kimmage shortly after 19:00 local time.
The boy was stabbed in the upper chest and was pronounced dead at the scene.
His mother, who is in her 40s and originally from the Middle East, sustained knife wounds during the incident and is in hospital.
Her injuries are not thought to be life-threatening.
Irish national broadcaster RTE has said that the Garda (Irish police) are treating the case as a personal tragedy at this stage.
They have appealed for any witnesses to contact them.
BBC News NI Ireland correspondent Shane Harrison told Good Morning Ulster: "Local people raised the alarm after reportedly hearing what sounded like a distressed woman.
"There were reportedly no signs, or no apparent signs of a break-in at the apartment.
"The woman is described as a medic of Iranian decent and is believed to be in her 40s."
The woman is separated from her husband who is also believed to be Iranian.
It is understood that police are seeking to interview all family members, neighbours and friends.
Police in Dublin are waiting to interview the mother of a three-year-old boy found stabbed to death in his home in the city on Monday.