The center has rescued more than 16,500 seals, otters, and sea lions in its 36-year history, center officials said.
The latest patient is a 111-pound juvenile male that was found on a dock in Santa Cruz near the boardwalk on June 15.
Rescuers watched the animal for several days before deciding that he needed medical treatment. He was taken to the Marine Mammal Center and is on antibiotics to treat what his caregivers believe may be a potentially fatal kidney disease, center officials said.
"The rescue of this sea lion, as well as all of our patients, is an amazing achievement and signifies the dedication and commitment we have to helping these animals and giving them a second chance at life," said Jeff Boehm, the center's executive director.
To mark the 10,000th sea lion patient, center staff has asked the public to help name him. To suggest a name, visit http://www.marinemammalcenter.org/about-us/News-Room/Latest-News/.10000 by Sunday.
A winning name will be chosen and announced on the center's website during the week of Aug. 1.