Norman West says Springtime Publishing did not sign a royalty agreement for the song Put It Back Together Again on Franklin's latest album.
Mr West, who has worked with Franklin for more than 20 years, is seeking unspecified damages to ensure future royalties.
Franklin's lawyers have not yet commented on the legal action.
Legal papers filed in Detroit show Mr West has asked a judge to order Springtime Publishing to sign the royalty agreement.
He has also accused Springtime Publishing of copyright infringement, claiming it has received money and other benefits over an earlier song, Watch My Back.
The songwriter says the legal claim was filed after private attempts to settle the dispute failed over the past year.
"These are two parties that have a long-standing working collaboration," West's lawyer told the Detroit News.
"Mr West has told me that he owes much of his career to Aretha Franklin and that he views her as both a mentor and a guiding force in his career."
Put It Back Together features on Franklin's latest album, Aretha: A Woman Falling Out of Love - her first studio album in about eight years.
The 69-year-old singer returned to performing in May after being admitted to hospital last year for an undisclosed ailment.
(Source: BBC)