A fine-structure (fs) analysis of the odd-parity Rydberg series of atomic zirconium, including the main low-lying mutually interacting configurations, has been performed for the first time, with the aid of a linked-parameter method of level fitting. A set of derived fs parameters, together with ab initio values calculated for comparison, and the leading eigenvector percentages of the levels were obtained. Many of the levels belonging to the 4d25s5p, 4d5s25p and 4d35p configurations are found to be incorrectly assigned. To confirm this major revision, specific mass shifts deduced from experimental isotope shift data available in the literature have been used as fingerprints. Finally, a complete set of predicted magnetic dipole and electric quadrupole hyperfine structure constants has been calculated for the known odd-parity levels in zirconium.