Molby returned for a second spell at Aggborough in October of last year following the departure of Ian Britton.
But with money tight at the Worcestershire club, Kidderminster have slumped to bottom position in League Two.
Youth-team manager Shaun Cunnington had been appointed caretaker manager, assisted by Gary Barnett.
Youngjohns said: "Both Jan and ourselves are united in our disappointment at the league position the club currently finds itself in - results haven't gone the way we would have hoped and Jan's task has been made all the more difficult by the horrendous injury problems we have suffered.
"The club needs a spark to re-ignite our season and Jan felt it would be best if someone else tried to do that. It was a difficult decision for him but we respect and understand his rationale."