The bicyclist, a 47-year-old Castro Valley man, was towing his daughter in a child bicycle trailer north in the southbound lanes of Danville Boulevard.
At about 2:15 p.m. a 45-year-old Alamo woman who was making a right turn from Camille Avenue onto Danville Boulevard failed to see the oncoming bicyclist and struck him and his daughter.
They were both wearing helmets and were taken to hospitals for treatment of minor injuries, Maguire said.
The driver of the car stopped and reported the accident. She is not considered at fault because the bicycle was traveling the wrong way.
Bicyclists are required to follow all of the same traffic laws as cars, Maguire said.