[Problem] To provide: a carbon fiber precursor fiber that can efficiently produce a carbon fiber at a low cost which is excellent in mechanical strengths even without an infusibilization treatment; a carbon fiber; and a method for producing the carbon fiber. [Solution] A carbon fiber precursor fiber of the present invention includes a polymer containing a constituent unit represented by General Formula (1) below: where in the General Fomula (1), X and Y each independently represent a divalent substituent, a single bond, or a structure forming a fused ring by sharing one side of two adjacent rings, and the divalent substituent is selected from the group consisting of -O-, -S-, -OSO-, -NH-, -CO-, -CH 2 -, and -CH(CH 3 ) 2 -.