Vocalist Cedric Bixler-Zavala announced the break-up on Twitter, seeming to blame the group's end on bandmate Omar Rodríguez-López's involvement with side project Bosnian Rainbows.
Bixler-Zavala formed progressive rock band The Mars Volta with Rodríguez-López in 2001 following the end of their previous band At the Drive-In.
"I can't sit here and pretend any more. I no longer am a member of Mars Volta," Bixler-Zavala tweeted.
"Thank u 2 all VOLTA fans u deserved more especially after the way u rooted for us on this album. I tried my hardest to keep it going. But Bosnian Rainbows was what we all got instead."
The Mars Volta released their sixth studio album Noctourniquet in March 2012, before going on a hiatus in September.
Bixler-Zavala added: "For the record I tried my hardest to get a full scale North American tour going for Noctourniquet but Omar did not want to.
"What am I suppose to do be some progressive house wife that's cool with watching their partner go f**k other bands? We owe it 2 fans to tour.
"Thank u a million times over for ever giving a f**k about our band."
Hours before the break-up announcement, Rodríguez-López had spoken to NME about the difficulty of working on new projects without Bixler-Zavala.
He said: "It's been very strange being without Cedric. It's one of those bittersweet moments, it's great for both of us because he's making this great solo record, which is more of an acoustic thing. I'm really excited to hear another side of him and to work on music without me.
"He's composing all the music, playing all the instruments, literally doing everything himself, rather than just singing over the top of my songs."
Last year, the pair reunited At the Drive-In and played several shows, including gigs at Coachella and Lollapalooza.
Watch The Mars Volta's video for 'Goliath' below: