The SUV was found abandoned with the child inside a short time later and the child appears to be OK, police said.
The incident happened around 3:15 p.m. when the driver left his car running as he ran into a West Seattle convenience store near 16th Ave. SW and SW Holden Street, said Drew Fowler with Seattle police.
Surveillance video shows the father parking right by the front door, and entering the store.
Moments later, a man walks up to the car, opens the front door, and begins to drive away.
Surveillance video provided by the store. Audio commentary provided by store clerk who witnessed event.
A store clerk said he and the father both noticed the thief get into the car
"That's when (the father) came out and started yelling at him, 'What's going on?!' " said the store clerk, who didn't want his name used. "He was in shock, I was in shock. I wasn't sure exactly what happened until he started chasing him and that's when I came out and called 911 right away."
The father ran out of the store and chased after the car.
"He was just yelling, 'My baby! My baby! My baby got stolen!' " the clerk said. "Then he ran across to the fire department and starting banging on the door over there as well."
Fowler said the thief likely did not know there was a child in the backseat.
Nineteen minutes later, King County sheriff's deputies located the abandoned SUV with the child still inside parked near 8th Ave. SW and SW 99th Street.
After an intense search of the neighborhood on the ground and in the air, Seattle police finally located and arrested their suspect near 17th Ave SW and SW Roxbury St. Estevean L. Sanchez is now being held in the King County Jail for investigation of kidnapping and theft.
Meanwhile, the father has been reunited with his child.
"Lots of hugs have already happened," Fowler said.