The incident occurred in the parking lot of the store in the 9200 block of Rainier Ave. S. around 6 p.m.
Witnesses said they saw several men arguing near the southeast corner of the parking lot before one of them opened fire.
The victim's condition was not known
A witness said the whole thing happened extremely fast.
"(It was) like he didn't know he was shot, the boy, and then he just collapsed," the woman said. "I heard seven or eight really fast shots, like boom, boom, boom, boom, boom.".
Police are now searching the area for the gunman. A description was not provided.
Police shut down Rainier Avenue in both directions in the 9200 block for investigation.
In a Friday night Tweet, Seattle Mayor Mike McGinn said, "Just briefed by Capt. Low at site of rainier beach shooting. Extra emphasis patrols this weekend."