A representative of Biel did not immediately respond to CNN's request for clarity on Biel's view of vaccines.
"Please say thank you to the brave @ jessicabiel for a busy and productive day at the California State House," said Kennedy, president of the Child Defense Fund, who opposes the bill.
In another photo, Kennedy and Biel posed with the Democratic Assembly Autumn Burke.
Biel commented on the post: "Good meeting with you both today."
"She was very strong and very knowledgeable," he said.
In April, the CDC confirmed that the United States was in the midst of the largest measles outbreak since the disease was declared eliminated in 2000.  Most cases in the United States have occurred in communities with low levels of vaccination against the virus, according to public health officials.