The second all-time leading goalscorer in the Frauen-Bundesliga, took charge in January but did not manage to make an impact with Switzerland exiting the Women's World Cup in the round of 16.
Switzerland have also failed to win their last four matches, which included a 7-1 loss to world champions Spain last month.
"It is with a heavy heart that I have decided to take this step in order to take the pressure off the team and the association in light of current events," Grings said on Thursday.
"It was an exciting time for me with many great experiences as national coach."
The SFA have not named Grings' successor.
"The change in coaching position is also an opportunity to provide new sporting impetus," SFA President Dominique Blanc said.
"We want to go into the future with our national team in the best possible position so that we can continue to capitalise on the positive mood for women's football in Switzerland."
Switzerland next host Sweden on December 1 in the Women's Nations League before visiting Italy on December 5. They sit at the bottom of League A Group four after losing all of their four games.
