Northampton, who have conceded 10 and scored just two during that run, have now taken the decision to part company with Edinburgh ahead of their next outing against Doncaster Rovers on September 9.
Chairman Kelvin Thomas told the club's official website: "Justin did a good job for us in difficult circumstances and achieved what was asked of him when he came in last season by retaining our League 1 status, for which we will always be grateful.
"However results overall haven't gone as well as any of us would have liked, but Justin is an honest and hard working individual and we wish him well for the future. David Kerslake will take temporary charge of the squad as we begin discussions to find our next manager.
"We do have some potential targets in mind and with a free weekend this weekend it does allow us some time. It is important that the focus of the squad is now on the game with Doncaster Rovers at Sixfields on Saturday September 9th."
Edinburgh was sacked by Gillingham in January after two years in charge and was appointed by Northampton a fortnight later.