The movie, in which several actors represent different stages of the musician's life and work, also earned nominations for director Todd Haynes, supporting actress Cate Blanchett, who plays one version of Dylan, and supporting actor Marcus Carl Franklin, 14, who plays another.
I'm Not There also claimed the first Robert Altman Award, named after the iconoclastic director of MASH who long-championed independent movies before his death in 2006.
Director Julian Schnabel's drama, The Diving Bell and the Butterfly, about a paralyzed French journalist who dictates a book by blinking, and Jason Reitman's comedy Juno, which tells of a young woman facing an unplanned pregnancy, earned four nominations each, including best movie and best director.
Also taking best film and director nods was Gus Van Sant's teenage skateboard drama, Paranoid Park. The final nomination among best films went to A Mighty Heart, about the search for slain Wall Street Journal reporter Daniel Pearl.
The final director nominee was Tamara Jenkins for drama The Savages, the story of two adult siblings who move their father to a nursing home. It earned four nominations overall.
"We have a huge array of talented filmmakers with movies in many different genres. It has been an exciting year for independent film and this shows a deep pool of talent," said Dawn Hudson, executive director of Los Angeles-based group Film Independent, which gives out the Spirit Awards.
Film Independent supports moviemakers working outside Hollywood's major studios or within the studios' specialty film divisions. The awards have become an important barometer for which low-budget and art films might compete for Oscars, Golden Globes or other honors in Hollywood's annual awards season.
Angelina Jolie was nominated for best leading actress playing Pearl's wife in Mighty Heart and relative newcomer Ellen Page earned a nod for Juno. Joining them were Sienna Miller for Interview, Parker Posey in Broken English and another newcomer, China's Tang Wei, in drama Lust, Caution.
In the category for best leading actor, Don Cheadle was nominated for his role as a radio disc jockey in Talk To Me and Philip Seymour Hoffman earned a nomination playing one of the siblings in The Savages.
Other best actor nominees included veteran Frank Langella in Starting Out in the Evening, Tony Leung, a veteran of Hong Kong movies, for Lust, Caution and Pedro Castaneda portraying a migrant worker in August Evening.
Joining Blanchett for supporting actress were Jennifer Jason Leigh for Margot at the Wedding, Anna Kendrick in Rocket Science, Tamara Podemski for Four Sheets to the Wind and Marisa Tomei with Before the Devil Knows You're Dead.
Supporting actor nominees with Franklin were Steve Zahn in Rescue Dawn, Chiwetel Ejiofor for Talk to Me, Kene Holliday in Great World of Sound, and Irrfan Khan in The Namesake.
Foreign film nominees included Romania's 4 Months, 3 Weeks and 2 Days, winner of the Cannes film festival's Palme d'Or, Israeli film The Band's Visit, Irish drama Once and two French films, Lady Chatterley and the animated Persepolis.
The Spirit Awards will be given out February 23 in a ceremony that will air on the Independent Film Channel.