Investigators said someone in the back hallway of the fired a shotgun.
Some of the pellets went through a hallway wall and struck the children, who were in bed.
The 12-year-old and an 11-month old suffered multiple gun shot wounds.
Their father was in the backyard when he heard the shotgun blast. They were both rushed to Beth Israel Hospital by the family.
The 11-month old was shot in the right back area and right leg. He is currently undergoing surgery. The 12-year old was struck in his left arm and his ring finger on his left hand.
Both victims are expected to survive.
The shooter is at large.
Police don't know at this point if the shooter lived in the apartment house.
Newark police ask that anyone with information about this or any other crimes continue to call the Department's 24-hour "Crime Stoppers" anonymous tip line at 877 NWK-TIPS (877 695-8477) or NWK-GUNS (877 695-4867).