Police say the boy was hit on the 200 block of South Avenue 54 after he ran into the street around 8 p.m. Wednesday.
The driver stopped briefly and then sped off.
Relatives say the toddler has a broken nose and other injuries, but is expected to be OK.
Police are looking for a white Ford F-150 truck with a camper shell and pink tail lights.
Anyone with information should call LAPD at (877) LAPD-24-7.
