"These questions must be answered because it is deeply disturbing to read reports of otherwise healthy children experiencing sudden paralysis," Boxer said in her letter.
In a statement emailed to the Associated Press, the CDC said Frieden had received the letter "and will be giving it careful consideration."
Doctors at Stanford University said earlier this week that they had found some instances of children suffering paralysis in one or more limbs. They also sought to temper concern, saying the cases were a rare phenomenon.
CDC officials amplified that point Thursday.
"At this time, CDC does not think the situation in California is a cause for public concern," Jamila H. Jones, a public health educator for the agency, said in an emailed statement before Boxer's letter became public. Her comments were not in direct response to the letter.
Jones said the CDC is concerned about the children who suffered what is described as acute flaccid paralysis, but the number of cases being investigated by California health officials fell within the expected rate within the overall population. She also said the CDC is monitoring the situation.
So far, state officials have not identified any common causes to suggest the cases are linked.
Earlier this week, Dr. Keith Van Haren at the Lucile Packard Children's Hospital at Stanford University said the disease seen in the children resembles polio, but is not the same as polio. Most of the children seen have so far not recovered use of their arms or legs.