Mandel Bruce Patinkin, known as Mandy, was born in Chicago, Illinois, on November 30, 1952, to Doris Lee "Doralee" (née Sinton) (1925–2014), a homemaker, and Lester Don Patinkin (1919–1972), who operated two large Chicago-area metal factories, the People's Iron & Metal Company and the Scrap Corporation of America. His mother wrote Grandma Doralee Patinkin's Jewish Family Cookbook. Patinkin's cousins include Mark Patinkin, an author and nationally syndicated columnist for The Providence Journal; Sheldon Patinkin of Columbia College Chicago's Theater Department, a founder of The Second City; Bonnie Miller Rubin, a Chicago Tribune reporter; Laura Patinkin, a New York–based actress; Louis Rosen, a New York–based composer; and Stacy Oliver née Patinkin, a writer and performer.
Patinkin grew up in an upper-middle-class family, descended from Jewish immigrants from Russia and Poland, and was raised in Conservative Judaism, attending religious school daily from the age of seven to 13 or 14 and singing in synagogue choirs, as well as attending the Camp Sura in Michigan. His father died of pancreatic cancer in 1972.
He attended South Shore High School, Harvard St. George School, and Kenwood High School (later renamed Kenwood Academy, where his teachers included Lena McLin), and graduated in 1970. He attended the University of Kansas and the Juilliard School (Drama Division Group 5: 1972–1976). At Juilliard, he was a classmate of Kelsey Grammer. When the producers of the sitcom Cheers were holding auditions for the role of Dr. Frasier Crane, Patinkin put Grammer's name forward.