Appointed in 2014, he led the side to two Muratti titles, as well as their first Island Games gold medal in 2015.
However, in a statement Petulla said disagreements with the JFA on how women's football should progress in the island made his position "untenable".
He added: "It's become clear that the priorities of the JFA differ from those of the current management team."
Assistant boss Charlie Petulla, goalkeeping coach Jason Carpenter and performance coach Jimmy Kelly have also stepped down.
Former Wales international Jodie Botterill, who has been named in the squad for this summer's Island Games in Gotland, will take charge of the side for their friendly against the Royal Navy on Saturday, alongside JFA community coach Daniel Seviour.
Speaking to BBC Radio Jersey, Simon Petulla added that the controversial cancellation of this year's Muratti match between Jersey and Guernsey had contributed to his decision.
"That's one of the main reasons - as a management team we felt the JFA should've fought tooth and nail to get that Muratti, instead of backing the GFA (Guernsey Football Association).
"Before we won the gold medal, people just left us alone to get on with our own thing, but as soon as we won the medal we had to run everything through the JFA, and things didn't get done."
Petulla's resignation comes exactly 100 days before the start of the Gotland Games, where Jersey will look to defend their women's football crown.
"There are some good people at the JFA as well, but there were certain people that we'd fallen out with over a period of time," he added.
"It shows me that they're not really out to keep the improvement that we've made over the years with the women's game and they're concentrating more on the men's game, and I think that's not fair in this day and age.
"I think with equality and the FA in England trying to really promote women's football, I think we need to be doing the same over here as well."
JFA chief executive Neville Davidson said in a statement: "Our immediate focus is on Saturday's fixture against the Navy. Thereafter we will look to appoint a new management team."
Analysis
Tim Pryor, BBC Radio Jersey sports editor
What a huge blow this is for women's football in Jersey, on the back of the cancellation of the Muratti.
Petulla and his coaching staff have raised the profile of the women's game in the island to the extent that there's as much of a buzz around their fixtures as the men's matches.
The team's first ever Island Games gold medal, achieved on home turf at Jersey 2015, was for many the standout, defining moment of the Games.
They leave behind a big hole that the Jersey FA will now need to fill at short notice, with the defence of the gold in Gotland this summer.
Simon Petulla has resigned as Jersey women's manager after falling out with the island's Football Association.