Lifetimes of intermediate-spin states in two rotational bands of Zr99 have been measured. These states were populated following the neutron-induced fission of U235 at the PF1B beamline of the Institut Laue-Langevin, Grenoble, during the EXILL-FATIMA campaign. The nucleus Zr9959 exhibits shape coexistence and lies precisely on the border of an abrupt change in ground-state deformation when going from N=58 to N=60, making its study interesting for understanding the mechanisms involved in the rapid onset of deformation here. The B(E2) values extracted for decays in the ν3/2 band allow quadrupole deformations of β2=0.34(1) and 0.26(3) to be determined for the 821.6- and 1236.6-keV members, whereas β2=0.32(3) was found for the 850.5-keV member of the ν3/2 band. Some of the excited states known in Zr99 have been reasonably described with interacting boson-fermion model (IBFM) calculations. Type-II shell evolution is proposed to play a major role in modifying single-particle energies in Zr99.