"The board feels the team should have accrued more points to date and that we need a new man in charge to ensure Premier League survival," chief executive Peter Storrie told the club's website.
Hart was offered the role of technical director, developing players from the ages of 18-21, but declined it.
The club said they would announce a replacement "very quickly and until that time the players will be led by first-team coaches Paul Groves and Ian Woan."
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Last month former Chelsea manager Avram Grant was appointed director of football, shortly after Saudi Arabian businessman Ali al Faraj's takeover of the club.
Israeli Grant has yet to receive his work permit but is rated the favourite to take over from Hart.
DROP ZONE
Former Leeds United and Nottingham Forest defender Hart steered Portsmouth away from the drop zone last season in a caretaker role before signing a two-year contract as permanent manager in July.
"The board would like to thank Paul for his work not only in keeping the club in the Premier League last season but also for his time in charge of youth development," added Storrie.
"Paul is a man of great dignity and we hoped he would stay and help us develop younger players on the fringes of the first team. We are genuinely sad to see him leave. Everyone at the club wishes him well for the future."
This season Portsmouth became the first English top-flight side in 79 years to lose their opening seven games of the campaign. They now have only two wins from 13 matches.
"Paul has worked under very difficult circumstances with the financial restrictions the club has faced since he took over," said Storrie.
Al Faraj bought 90 percent of the club's shares last month from Sulaiman al Fahim who had taken over in August but struggled to refinance Portsmouth's mounting debts.
Grant, who replaced Jose Mourinho as Chelsea manager in September 2007 before being sacked the following May, was also technical director at Portsmouth from June 2006 to July 2007.
