The mother was dying when found by volunteers looking for new sea turtle nests, but the calf was alive, the South Florida Sun Sentinel reported Tuesday.
The adult mammal was "in very bad shape, very thin and emaciated," said Dr. Charles Manire, the director of research and rehabilitation at Loggerhead Marinelife Center.
The calf, which was two or three days old, was euthanized because a calf that young cannot survive without its mother, Manire said.
The bodies were taken to the Gumbo Limbo Nature Center in Boca Raton for necropsies. Authorities said the mother might have had heart disease, which is common in the species.