Emergency responders received the call at 9:49 a.m. about the crash on Market Street at Third Street, police spokesman Officer Albie Esparza said.
The bicyclist, a man, was riding on Market with a woman riding on his handlebars when he smashed into the back of the FedEx truck, Esparza said.
The man suffered serious injuries and was taken to a hospital, fire officials said. His injuries were not life-threatening, according to Esparza.
The woman on the handlebars was uninjured, Esparza said.
The crash caused delays on Market Street as emergency crews worked the scene. Eastbound Market Street was briefly shut down, according to police.