All four were taken to area hospitals.
No one has been arrested, but police are looking for a black man wearing a grey shirt in a grey Nissan Altima who left westbound from the scene.
The shooting, which happened at Smokey’s Paradise Food Mart, was reported as a drive-by in the police phone call.
Police were sent to 5300 block of East Rosedale at 5:39pm local time (11:39pm BST).
One 3-year-old, a boy, was shot in the leg and the other, a girl, was shot in the arm, but none of their conditions are life-threatening.
This shoot-out comes just a day after four people were shot dead near Corpus Christi, Texas, after an argument broke out at a at a 1-year-old’s birthday party.
Those killed were identified as Juan Espinoza Sr, 62, and his grandsons Juan Sandoval III, 20, Jeremy Sandoval, 22, and Nicky Sandoval.
Juan Espinoza Jr, 43, was airlifted to a hospital in Corpus Christi, where he is in a critical condition.
Witnesses told investigators: “an argument over something real small and it escalated real quickly to where guns were involved.”
Fort Worth is a city near Dallas in North Central Texas.
The state witnessed a school shooting in Santa Fe in May, when 10 people died and 14 people were injured.