She said no one had accused her of hitting a staff member and she had never been approached by Ministerial Services - which deals with ministerial staff - about such allegations.
Mr Mallard told reporters after the committee that he believed a former staff member had left the office after being hit on the head.
He said he had heard the allegation indirectly from "a very good source."
The alleged incident did not happen this year but happened this term. It was his understanding the staff member left after the alleged incident.
Ms Parata was being questioned by the committee about the 2014 - 15 estimates of appropriation. Mr Mallard started asking questions about bullying before asking Ms Parata whether she had ever hit a staff member.
Later the minister told reporters: "I would prefer that Vote Education focused on what we are here to do which is to talk about what we are doing with all the taxpayers' money and have that reported."