Town currently sit just one place and one point above the bottom four, a position not acceptable for either the fans or the board.
No statement has yet been issued by the club, nor is it known what will happen with regards Groves' playing contract - which does not expire until the summer.
Assistant manager Graham Rodger has been placed in temporary charge.
We'll bring you more on this story later in the day.
We would also like to wish Paul Groves well for his future plans and thank him for the excellent service he gave the club as a player.