The Sunyaev-Zeldovich (SZ) effect is the inverse Compton-scattering of cosmic microwave background (CMB) photons by hot electrons in the intervening gas throughout the universe. The effect has a distinct spectral signature that allows its separation from other signals in multifrequency CMB datasets. Using CMB anisotropies measured at three frequencies by the BOOMERanG 2003 flight we constrain SZ fluctuations in the 10 arcmin to 1 deg angular range. Propagating errors and potential systematic effects through simulations, we obtain an overall upper limit of 15.3 uK (2 sigma) for rms SZ fluctuations in a broad bin between multipoles of of 250 and 1200 at the Rayleigh-Jeans (RJ) end of the spectrum. When combined with other CMB anisotropy and SZ measurements, we find that the local universe normalization of the density perturbations is sigma-8(SZ) < 0.96 at the 95% confidence level, consistent with sigma-8 determined from primordial perturbations.