It happened on May 12 on the 3700 block of Germantown Avenue.
Police say the 32-year-old father and another man exchanged words before he was shot four times in the leg.
Video released by police shows the gunman opening fire in front of the infant.
The father was taken to an area hospital and listed in critical condition.
Anyone with information on the suspect is asked to call police at 215-686-TIPS.