The stranger tried to grab the boy away from his grandmother's hand about 9:30 a.m. at 5th Ave. and Broad Street while the boy's family was participating in the Susan G. Komen Race for the Cure near Seattle Center, Detective Mark Jamieson said.
The child's aunt confronted the man and told him to let go, which he did, police said.
The man took off running and the boy's father and uncle followed him to 4th and Cedar St. where they told an officer directing traffic what happened.
The officer took the man into custody and patrol officers arrived on the scene.
The boy's family said another family approached them while they were following the suspect and told them that the suspect had attempted to grab another child earlier on the event route.
Officers were unable to locate the earlier victim, witnesses, or family.
The child was not injured during the incident, police said.
The man was booked into the King County Jail for investigation of kidnapping.