Penney, who took over from Paul Trollope on January 10, guided the Pirates to just two wins in 13 games and leaves with the club languishing 23rd in the League One table, five points from safety.
Captain Stuart Campbell will take control of first-team duties until the end of the season, starting with the trip to Tranmere on Tuesday.
A statement on the club's official website said: "We are all very disappointed and sad that the appointment of Dave Penney has not brought us the results and change of direction that we have been looking for.
"With 12 games left there is still a chance to get ourselves out of this situation and try and secure our League One status.
"We wish Stuart Campbell every success for the remainder of the season, and would call on all fans to back him, and the team, as he tries to rescue our season."
Source: PA
Source: PA