Stoger has led Cologne since 2013 and, after winning promotion, secured European football for the first time in 25 years last season with a fifth-placed finish.
However, the 2017-18 campaign has been an abject failure, with Cologne collecting three points from their opening 14 games, and facing elimination from the Europa League should they fail to beat Red Star Belgrade on Thursday.
Last weekend's loss to Hertha Berlin appeared to be the final straw for Stoger, who has mutually agreed to bring his four-year tenure to an abrupt end.
"It was clear to us on Friday that the Schalke match would be our last," Stoger told the club's official website.
"We decided to wait until Sunday to communicate this in order to fully concentrate on the match.
"It is in the best interest of the club and especially the team that a decision was made and clarity restored.
"To the players, the staff at the club, the fans, and the city of Cologne: you have grown dear to the hearts of Manni Schmid [his assistant] and I, we will keep our fingers crossed that my successor manages to keep Cologne in the Bundesliga."
Achieving survival looks to be a huge task for whoever replaces Stoger, as Under-19 coach Stefan Ruthenbeck takes temporary charge until the mid-season break.
"We would like to thank Peter for four-and-a-half years of excellent work," the club's chief executive Alexander Wehrle said. "Peter has written an unprecedented success story with Cologne.
"Both Peter and us have felt in recent days that our joint path was coming to an end, regardless of the result against Schalke.
"The team is now, more than ever, expected to build on the hope that was created through that result.
"I refuse to talk about [relegation] to the second league at this point. There are still 20 league matches to play and it is our responsibility to attain the maximum out of what remains."