The suspects are being held on suspicion of weapons possession, among other possible charges.
Police recovered 21 vehicles, many with bullet holes or US licence plates, and a total of 54 guns at various points in the city where the battles broke out, Agustin Perez Aguilar, a spokesman for the state public safety department, said.
Heavily armed federal police patrolled across Tijuana following the gunfight.
Soldiers and police guarded the city's main hospital where the wounded were being treated to prevent any attempt by drug gangs to pull them out.
Daniel de la Rosa, Baja California's state police chief, said fresh troops from Mexico City were arriving in Tijuana, which borders San Diego, California.
Felipe Calderon, Mexico's president, has sent thousands of troops to Tijuana and Baja California state since taking office in December 2006.
Some 25,000 soldiers and federal police are deployed to fight cartels in drug hot spots across Mexico.
But despite the military crackdown on drug trafficking, nearly 3,000 people died in Mexico's drug war in 2007.
A further 900 have already been killed in the first quarter of this year.