The guitarist, who worked with the band on their debut album and first US tour, was just 64 and his cause of death has not yet been revealed.
The band wrote on Twitter: "We of the RHCP family would like to wish Jack Sherman smooth sailing into the worlds beyond, for he has passed. Jack played on our debut album as well as our first tour of the USA.
"He was a unique dude and we thank him for all times good, bad and in between. Peace on the boogie platform."
Bassist Flea commented "Love to Sherm" on the post.
Sherman replaced guitarist Hillel Slovak on group's self-titled debut album and was a cowriter on its follow-up, 1985's 'Freaky Styley.
However, he was replaced by Slovak before the album was released.
He went on to contribute to 'Mother’s Milk' and 'The Abbey Road EP' but was left out when the band was inducted into the Rock & Roll Hall of Fame eight years ago.
Sherman told Billboard at the time: "I'm being dishonoured, and it sucks. It's really painful to see all this celebrating going on and be excluded. I'm not claiming that I've brought anything other to the band… but to have soldiered on under arduous conditions to try to make the thing work, and I think that's what you do in a job, looking back. And that's been dishonoured."
He has also worked on Tonio K.’s 'Notes from the Lost Civilization', Bob Dylan’s 'Knocked Out Loaded', and records by George Clinton and Feargal Sharkey.
