The 66-year-old has enjoyed a two-decade association with the club as both a player and a coach, but he now believes that a change is needed at the New Meadow.
The Shrews are currently one point above the relegation zone in the table following five defeats in their last six games.
"It's a very sad decision. It's a club that I've really enjoyed working at, it's a club that gave me my first opportunity in management so I'll always appreciate that and will always be close to the club," Turner told Shrewsbury's official website.
"I just felt it wasn't necessarily just Saturday. I think there's been a sequence of results where for several weeks now I thought I could improve things.
"I thought I was the right man to get the results going and it hasn't materialised so I felt that there was a need for a decision to be made. I don't think we could just carry on in the same vein and that decision I reached was I would step down as team manager of Shrewsbury Town."
Shrewsbury return to League One action on Saturday when they make the trip to Swindon Town.