The Shaymen lie bottom of the National League, 10 points adrift of Boreham Wood in 20th, following a 6-3 defeat by Braintree on Saturday.
Former Oldham Athletic manager Kelly, 36, was appointed at Halifax on 1 October and won two of his 10 games in charge in all competitions.
A club statement said a further announcement would follow shortly.
"Notwithstanding a backdrop of difficult circumstances and a short time period, it's been felt that an up-lift in performance and results has not been forthcoming - despite further first-team investment," the statement added.
Kelly's only previous managerial role was at Oldham, but he was replaced by David Dunn in September after just over four months - and nine games - in charge at Boundary Park.
Halifax conceded 37 goals in 10 games under Kelly, including seven against both Grimsby and Cheltenham.
Manager Darren Kelly has left FC Halifax Town by mutual agreement after just 47 days in charge.