The experienced runner appeared to bump Picken as the Bulldog and his direct opponent Brendon Goddard ran from the ground at the 10-minute mark of the third quarter.
Walsh was between the two players and hit Picken side on as the players approached the interchange bench.
The club was asked to explain Walsh’s actions on Monday afternoon and League football operations manager Adrian Anderson said the runner's written apology to Picken had been taken into account when determining the penalty.
"Runners have a responsibility to deliver messages in an appropriate manner, then get off the field straight away," Anderson said.
“There should not be contact or interaction with any opposition player or AFL umpire.”
Under the AFL Player Rules, the maximum sanction that can be imposed is $10,000 for a first offence, while a suspension or a sanction of up to $25,000 may apply for any further breach.
The battle between the Goddard and Picken lasted most of the game and grew heated at times.
A third-quarter marking contest between the two players was assessed by the match review panel on Monday but Goddard was decreed to have been looking at the ball when he made high contact with Picken.
