The former Motherwell boss has left the Robins by mutual agreement with his assistant, David Byrne, taking charge of team affairs until further notice.
A brief statement on the club's official website read: "The board would like to place on record their thanks for the professionalism that Maurice brought to the club in so many areas during his tenure."
Malpas' position became untenable after his side suffered defeats in the FA Cup and Johnstone's Paint Trophy this week.
Town lost to Blue Square Premier League side Histon in an FA Cup first round tie last weekend, before crashing out of the Johnstone's Paint Trophy on Wednesday at Brighton.
Malpas' side have won only four of their 14 League One matches so far this season and are currently 17th in the table, only three points above the relegation zone.