The South African has made over 160 appearances for the Aviva Premiership side since joining them in 2007.
"Mike has been a wonderful player for Bath," Gold is quoted as saying by Sky Sports News.
"On and off the field he is the ultimate professional, and his good nature will be missed greatly.
"We completely respect his decision to move on though, and he goes with all our best wishes as he looks to continue his career elsewhere."
Claassens is expected to join French side Toulon at the end of the season.