New experimental cross sections are presented for Zr90(n,α)87mSr, Zr90(n,x)89mY, Zr90(n,p)90mY, Zr90(n,2n)89Zr, Zr90(n,2n)89mZr, Zr91(n,nα)87mSr, Zr91(n,x)90mY, Zr91(n,p)91mY, Zr92(n,x)91mY, Zr92(n,p)92Y, Zr94(n,α)91Sr, Zr94(n,x)93Y and Zr94(n,p)94Y reactions. These have been obtained with the activation technique using gamma-ray spectrometry and irradiations at the IRMM Van de Graaff laboratory. The new data were obtained in the energy range from 14 to 21 MeV. In nearly all cases this work provides the first data above 15 MeV and for the Zr92(n,x)91mY and Zr91(n,nα)87mSr reactions no earlier data were reported. The experimental results are compared with model calculations using the TALYS code to obtain a first indication of the impact of the new data on modeling of n+Zr reactions.