We use a suite of N-body simulations that incorporate massive neutrinos as an extra-set of particles to investigate their effect on the halo mass function . We show that for cosmologies with massive neutrinos the mass function of dark matter haloes selected using the spherical overdensity ( SO ) criterion is well reproduced by the fitting formula of Tinker et al . ( 2008 ) once the cold dark matter power spectrum is considered instead of the total matter power , as it is usually done . The differences between the two implementations , i.e . using P _ { cdm } ( k ) instead of P _ { m } ( k ) , are more pronounced for large values of the neutrino masses and in the high end of the halo mass function : in particular , the number of massive haloes is higher when P _ { cdm } ( k ) is considered rather than P _ { m } ( k ) . As a quantitative application of our findings we consider a Planck -like SZ-clusters survey and show that the differences in predicted number counts can be as large as 30 \% for \sum m _ { \nu } = 0.4 eV . Finally , we use the Planck -SZ clusters sample , with an approximate likelihood calculation , to derive Planck -like constraints on cosmological parameters . We find that , in a massive neutrino cosmology , our correction to the halo mass function produces a shift in the \sigma _ { 8 } ( \Omega _ { m } / 0.27 ) ^ { \gamma } relation which can be quantified as \Delta \gamma \sim 0.05 and \Delta \gamma \sim 0.14 assuming one ( N _ { \nu } = 1 ) or three ( N _ { \nu } = 3 ) degenerate massive neutrino , respectively . The shift results in a lower mean value of \sigma _ { 8 } with \Delta \sigma _ { 8 } = 0.01 for N _ { \nu } = 1 and \Delta \sigma _ { 8 } = 0.02 for N _ { \nu } = 3 , respectively . Such difference , in a cosmology with massive neutrinos , would increase the tension between cluster abundance and Planck CMB measurements .