Motherwell sit fifth in the Scottish Premiership but some fans had turned against Kettlewell, particularly in the wake of the Scottish Cup defeat by St Johnstone on January 18.
After another defeat in Perth on Saturday, this time in the league, the former Ross County manager decided he has had enough of the criticism.
Motherwell confirmed their board of directors had “very reluctantly” accepted the 40-year-old’s resignation.
A statement added: “Stuart approached chief executive Brian Caldwell on Monday morning to explain why he wished to resign. Stuart explained that some of the personal abuse was now affecting his family, to the point where they didn’t wish to attend games.
“As a result, he felt it would be best if he tendered…