"Harry Potter" star Emma Watson said Wednesday on Twitter: "heard about Joni and haven't been able to concentrate all morning. So hope she's doing ok."
Kiss lead singer Paul Stanley tweeted a recent picture of himself and the Rock and Roll Hall of Famer, telling his followers to send her love and prayers.
Kevin Bacon tweeted that he was "sending good wishes today to one of the finest singing, song-writing, guitar playing artists in history."
Boy George, Bill Idol and Tori Amos were also among the well-wishers.
Mitchell, 71, was found unconscious in her home Tuesday night and taken to a hospital by ambulance, according to her Twitter account and website. She was later in intensive care and undergoing tests.
Her representatives did not immediately respond to phone and email messages and there was no further word on her condition Wednesday.
Mitchell told Billboard magazine last year that she has a rare skin condition, Morgellons disease, which prevents her from performing.
Mitchell has received eight Grammy Awards, including a lifetime achievement award in 2002. She was inducted into the Rock and Roll Hall of Fame in 1997.
The native of Fort Macleod, Alta., is also a member of the Canadian Music Hall of Fame and the Canadian Songwriters Hall of Fame.
She has a star on Canada's Walk of Fame in Toronto and a commemorative stamp, and is a companion of the Order of Canada.
Mitchell began her career as a street musician before moving to Southern California, where she became part of the flourishing folk scene in the late 1960s.
Her second album, "Clouds," was a breakthrough with such songs as "Both Sides Now" and "Chelsea Morning," winning Mitchell the Grammy for best folk performance. Her 1970 album, "Ladies of the Canyon," featured the hit single "Big Yellow Taxi" and the era-defining "Woodstock." The following year, she released "Blue," which ranks 30th on Rolling Stone magazine's list of the "500 Greatest Albums of All Time."
Mitchell has released 19 original albums, the most recent in 2007. The anthology released last year, "Love Has Many Faces: A Quartet, A Ballet, Waiting to Be Danced," features remastered versions of 53 of her songs.
Her musical style integrates folk and jazz elements, and she counts jazz giants Charles Mingus and Pat Metheny among her past collaborators.
As with music, Mitchell taught herself painting as a child and has produced hundreds of works in ink, watercolour and acrylic.