Pennock kept the club in the National League on the final day of the season having pulled the Bluebirds out of trouble.
Now they are searching for a new boss and assistant with Jamie Day also departing Holker Street.
A club statement confirmed the news and say they will begin work looking for a new manager straight away.
“Since the season came to an end discussions have been held between the management duo and the clubs management, with the decision made to part company,” it read.
“Ady joined the Bluebirds in October last year following the departure of Micky Moore, with Jamie Day joining him in February.
“Everyone at Barrow AFC would like to thank Ady & Jamie for all of their efforts to keep the club in the National League last season and wish them both well for the future.
“The process of selecting a new manager will now begin immediately, details will follow shortly.”
Barrow had a poor season, with the club going five months without a home win from November through to April.
But they retained their National League status. Despite defeat on the final day to Chester, Woking’s home reverse against Dover meant Barrow were safe.