A statement released by the Cumbrian part-timers said: "The board, having fully considered the current situation at the club, feel that in the best interests of the future of Barrow AFC a new man is needed at the helm.
"The position will be advertised shortly in the national press with a north-west based manager with a proven semi-professional track record at this level or above, the ideal choice.
"The board would like to thank Lee for his untiring efforts over his two-and-a-half years as manager at Holker Street and in the several years prior to that as assistant to Kenny Lowe."
Turnbull combined his role as manager at Barrow with his duties at Glanford Park.
Paul Raven, who has been Turnbull's assistant, will take charge of the side on a caretaker basis.