The collision occurred around 7:30 a.m. at Broadway and The Embarcadero, police spokesman Albie Esparza said.
Police received initial reports that a third pedestrian had also been hit, but only two people were taken to a hospital, police Officer Gordon Shyy said.
He said the woman and child were hospitalized with injuries that do not appear to be life-threatening.
The driver of the truck involved in the collision stopped at the scene and cooperated with the police investigation, Shyy said.
Police do not believe alcohol or drugs played a role in the incident.