The decision was announced after the Tractor Boys were held to a goalless draw by Barrow in the FA Cup.
Cook, who was appointed boss at Portman Road in March on a contract until 2023, was tasked with winning promotion but they are currently 11th in League One.
Ipswich CEO, Mark Ashton, said: "Firstly, we would like to thank Paul and his team for their efforts in what has been a difficult transition period for everyone.
"I know how much Paul wanted to succeed at this club. However, following discussions with the board, we have decided a change is needed for our long-term interests.
"At this moment, there is no one lined-up to replace Paul. There will be an extensive search to find the best replacement for the club.”
Cook led the Spireites to the League Two title and the JPT final in 2014 and the League One play-offs the following year.