The Sandgrounders are bottom of the Conference having won only four league games under Cook's leadership, and his exit follows three defeats over Christmas.
Cook only took over at Haig Avenue in the summer from Liam Watson following the club's decision to go full-time.
Southport chief executive Haydn Preece said the club were looking to name a replacement quickly in order to give the new manager time to bring in new signings during the transfer window.