The incident happened in the closing stages of Ipswich’s goalless draw at home to Northampton.
After Judge had been given a yellow card, the Ipswich player approached the referee.
A confrontation between the two briefly ensued, with Drysdale appearing to move his head towards Judge, before Ipswich’s Flynn Downes and Jack Lankester and Northampton defender Lloyd Jones stepped in and calmed the situation.
There was a red card shortly afterwards, with Downes picking up a second yellow card.
Additional reporting by PA.