The search began around 6:45 p.m. Tuesday after four migrants swam ashore near the Naval Auxiliary Landing Field on the island, which is a military training site.
The migrants said their boat was stranded after its engine caught fire and some of the group paddled it to shore.
On Wednesday morning, Border Patrol and Coast Guard teams began an air and water search of the island. By 5 p.m., 15 other migrants had been located.
The group consisted of 16 men and three women aged from 17 to 45. All were Mexican nationals illegally present in the United States. Two were identified as smugglers.
One man in the group complained of abdominal pain and was flown to the Naval Air Station North Island, then transported to a local hospital for treatment. An additional four people in the group were treated by agents for minor injuries.
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