The growth of structure in the Universe begins at the time of radiation–matter equality, which corresponds to energy scales of ∼0.4 eV. All tracers of dark matter evolution are expected to be sensitive to neutrino masses on this and smaller scales. Here we explore the possibility of using cluster number counts and power spectrum obtained from ongoing Sunyaev–Zel’dovich (SZ) surveys to constrain neutrino masses. Specifically, we forecast the capability of ongoing measurements with the Planck satellite and the ground-based South Pole Telescope (SPT) experiment, as well as measurements with the proposed Epic satellite, to set interesting bounds on neutrino masses from their respective SZ surveys. We also consider an Atacama Cosmology Telescope (ACT)-like cosmic microwave background (CMB) experiment that covers only a few hundred deg2 also to explore the trade-off between the survey area and sensitivity and what effect this may have on inferred neutrino masses. We find that for such an experiment a shallow survey is preferable over a deep and low-noise scanning scheme. The precision with which the total neutrino mass can be determined from SZ number counts and power spectrum is limited mostly by uncertainties in the basic cosmological parameters, the mass function of clusters and their mean gas mass fraction; all these are explicitly accounted for in our statistical Fisher matrix treatment. We find that projected results from the Planck SZ survey can, in principle, be used to determine the total neutrino mass with a (1σ) uncertainty of 0.28 eV, if the detection limit of a cluster is set at the 5σ significance level. This is twice as large as the limits expected from Planck CMB lensing measurements. The corresponding limits from the SPT and Epic surveys are ∼0.44 and ∼0.12 eV, respectively. Mapping an area of 200 deg2, ACT measurements are predicted to attain a 1σ uncertainty of 0.61 eV; expanding the observed area to 4000 deg2 will decrease the uncertainty to 0.36 eV.