A 19-month-old girl travelling on a bus with her mother was hit on the back of the head and shouted at by a man, police said.
The incident happened on the number 29 bus from Luton town centre to St Margaret’s Avenue on 4 February.
Bedfordshire Police said the child had been crying while in a pushchair next to her mother.
“This is a truly shocking incident where a baby was assaulted on a bus in broad daylight,” said PC Carolyn Hoare.
“We will not tolerate this kind of behaviour in our county.”
The force has released CCTV images of a man it would like to speak to in relation to the assault.