It happened around 2am Sunday at the Bayridge Apartments in the 3000 block of East League City Parkway.
According to police, Roger Anthony Winston and another male became involved in a disturbance at the apartment.
Officials said Winston fired two rounds from a shotgun at the other male and missed him, but struck the child in the arm.
The toddler was asleep on a couch when the shooting happened.
Life Flight airlifted the child to UTMB in Galveston in critical condition.
No one else was injured.
The alleged shooter fled the scene, but authorities said they caught up with him a short time later.
Winston, 21, is charged with aggravated assault. Bond was set at $100,000.
Anyone with additional information about this case is asked to contact Det. Marty Grant at 281-338-4173.