The club announced their decision on Tuesday, ending the father-son selection's four-year spell at Punt Road.
The son of Tigers best and fairest Chris, Naish has played nine games in the yellow and black since making his debut in 2019, featuring in Damien Hardwick's side on six occasions this season.
Richmond' football talent manager Blair Hartley lauded Naish for his service to the club since joining via the 2017 draft.
“We would like to thank Patrick for his hard work and commitment to our football program across the past four years,” Hartley said via the club's announcement.
“Patrick has played his part in our recent success, and we wish him all the best for his future endeavours.”