The results from weak gravitational lensing analyses are subject to a cosmic variance error term that has previously been estimated assuming Gaussian statistics . In this letter we address the issue of estimating cosmic variance errors for weak lensing surveys in the non-Gaussian regime . Using standard cold dark matter model ray-tracing simulations characterized by \Omega _ { m } = 0.3 ,~ { } \Omega _ { \Lambda } = 0.7 ,~ { } h = 0.7 ,~ { } \sigma _ { 8 } = 1.0 for different survey redshifts z _ { s } , we determine the variance of the two-point shear correlation function measured across 64 independent lines of sight . We compare the measured variance to the variance expected from a random Gaussian field and derive a redshift-dependent non-Gaussian calibration relation . We find that the ratio between the non-Gaussian and Gaussian variance at 1 arcminute can be as high as \sim 30 for a survey with source redshift z _ { s } \sim 0.5 and \sim 10 for z _ { s } \sim 1 . The transition scale \vartheta _ { c } above which the ratio is consistent with unity , is found to be \vartheta _ { c } \sim 20 arcmin for z _ { s } \sim 0.5 and \vartheta _ { c } \sim 10 arcmin for z _ { s } \sim 1 . We provide fitting formula to our results permitting the estimation of non-Gaussian cosmic variance errors and discuss the impact on current and future surveys . A more extensive set of simulations will however be required to investigate the dependence of our results on cosmology , specifically on the amplitude of clustering .