It's part of a one-year pilot program implemented by the airport to give visitors an alternative to taxis.
The cab drivers say the move presents unfair competition that threatens their livelihoods.
"We are struggling right now, we are really struggling now," said Steve Sajjad who says he's been driving a cab for 34 years.
Sajjad said cabbies like him are subjected to a lot more regulations and oversight compared to Uber and Lyft drivers.
"We have to have commercial licenses and business licenses and carry $1 million insurance for passengers. Passengers are safer in our taxis as our cars are constantly inspected. We charge the same every day at all times something Uber and Lyft don't do - they hide their prices," said Sajjad.
According to Sajjad, taxi drivers must pass yearly background checks conducted by the San Diego County Sheriff's Department.
Uber and Lyft also require background checks for all of their drivers.
"Riders and drivers in San Diego voiced their strong support for ridesharing options at Lindbergh Field and we look forward to applying for the permit," Chris Ballard, GM Uber San Diego, stated Thursday.
Lyft sent a statement that read in part: "We're excited to announce that travelers will be able to request a Lyft ride at San Diego International Airport."