The Dec. 13 incident was captured on video and circulated on social media, reports The Lafayette Journal & Courier.
The video reportedly showed the parent repeatedly hitting a 16-year-old student with a sock that contained an object. It was also reported that two other students joined in on the attack.
Lafayette Police Lt. Randy Sherer says the battery on the bus may be connected to an earlier fight.
The case has been sent to the prosecutor's office for further review.