Chairman Paul Scally will take over the day-to-day running of the Kent side.
A club statement said: "It is with deep regret that the finances at the club means we are no longer able to keep Mr Hover with us.
"The club would like to take this opportunity to wish Graham all the very best for the future and thank him for all the hard work he put into the football club during his time with us.
"The club will not be replacing his position as chief executive; instead chairman Paul Scally will revert back to the chairman/chief executive role with immediate effect."
The Gills, with reported debts of more than £9million, are currently just one point and one place above the League One drop zone.