According to CNN, most of the victims do not have life-threatening injuries, but three of them require urgent medical attention.
"@SDLifeguards and SDFD firefighters at Cabrillo Monument on the overturned vessel incident. 24 persons were on board. Many patients transported to hospitals. @USCG Fed Fire & many other agencies assisting", the rescue service tweeted.
The San Diego Lifeguard later confirmed the number of casualties.
Media reports say that the victims of Sunday's incident were sailing in a panga - a medium-sized fishing vessel often used by smugglers to illegally bring people from Mexico into the United States.
The cause of the accident remains unknown.