The Wings are without a league win since mid-October and sit in the relegation zone.
Fazakerley took over in March 2015 and guided the team to safety at the end of last season.
Operations manager Barry Hobbins said: “We’re disappointed that we’ve had to make a change but we felt we had to give ourselves the best chance possible of staying up.
“We enjoyed a good run in the FA Cup this season but the league is our priority and we need to get back to winning ways very quickly.
“Loui has been a fantastic servant to the club, both as a player over a number of seasons and as a manager in the past year or so. We wish him all the best in the future.”
Fazakerley has made 219 appearances for the club.
The club can confirm that Matt McEntegart and Paul Barnes have also departed.