We quantify the bias and scatter in galaxy cluster masses M200 and concentrations c derived from an idealized mock weak gravitational lensing (WL) survey, and their effect on the cluster mass–concentration relation. For this, we simulate WL distortions on a population of background galaxies due to a large (≈3000) sample of galaxy cluster haloes extracted from the Millennium Simulation at z≃ 0.2. This study takes into account the influence of shape noise, cluster substructure and asphericity as well as correlated large-scale structure, but not uncorrelated large-scale structure along the line of sight and observational effects (e.g. the source redshift distribution and measurement, and measurement of galaxy ellipticities). We find a small, but non-negligible, negative median bias in both mass and concentration at a level of ∼5 per cent, the exact value depending both on cluster mass and on radial survey range. Both the mass and concentration derived from WL show considerable scatter about their true values. This scatter has, even for the highest mass clusters of M200 > 1014.8 M⊙, a level of ∼30 per cent and ∼20 per cent for concentration and mass, respectively, and increases strongly with decreasing cluster mass. For a typical survey analysing 30 galaxies per arcmin2 over a radial range from 30 arcsec to 15 arcmin from the cluster centre, the derived M200−c relation has a slope and normalization too low compared to the underlying true (3D) relation by ∼40 per cent and ∼15 per cent, respectively. The scatter and bias in mass are shown to reflect a departure at large radii of the true WL shear/matter distribution of the simulated clusters from the NFW profile adopted in modelling the mock observations. Orientation of the triaxial cluster haloes dominates the concentration scatter (except at low masses, where galaxy shape noise becomes dominant), while the bias in c is mostly due to substructure within the virial radius.