The next generation of space-based telescopes used for weak lensing surveys will require exquisite point spread function (PSF) determination. Previously negligible effects may become important in the reconstruction of the PSF, in part because of the improved spatial resolution. In this paper, we show that unresolved multiple star systems can affect the ellipticity and size of the PSF and that this effect is not cancelled even when using many stars in the reconstruction process. We estimate the error in the reconstruction of the PSF due to the binaries in the star sample both analytically and with image simulations for different PSFs and stellar populations. The simulations support our analytical finding that the error on the size of the PSF is a function of the multiple stars distribution and of the intrinsic value of the size of the PSF, i.e. if all stars were single. Similarly, the modification of each of the complex ellipticity components (e(1); e(2)) depends on the distribution of multiple stars and on the intrinsic complex ellipticity. Using image simulations, we also show that the predicted error in the PSF shape is a theoretical limit that can be reached only if large number of stars ( up to thousands) are used together to build the PSF at any desired spatial position. For a lower number of stars, the PSF reconstruction is worse. Finally, we compute the effect of binarity for different stellar magnitudes and show that bright stars alter the PSF size and ellipticity more than faint stars. This may affect the design of PSF calibration strategies and the choice of the related calibration fields.