The 38-year-old ends his 18-month stay at the Vanarama National League South club.
Braintree finished the season 17th - ending their campaign with 1-0 home defeat against relegated Billericay Town three days ago.
Maxwell had been in charge of the Iron since November 2020.
But after a meeting with club chairman Lee Harding, his departure was announced as Maxwell bid farewell on social media.
He wrote: "Decided to part ways very amicably tonight. Been hell of a season at Braintree Town.
"So many positives, as a team and personal. Huge thanks to everyone at the club, pleased I put Braintree in a good light once again.
"We created something good an honest with very little an punched above our weight.
"Some of the players were unknowns and now are getting offers they can’t turn down. We came in with Braintree 0 points from 7 games and dragged them off the bottom, saving the club before Covid.
"I’m proud to have saved them again! My staff and players [are] unreal. Thank you."
Chairman Lee Harding added: "Our thanks go to Ryan for steering the Club through a difficult season after the Covid restrictions. We wish him every success in his future career."