The structure of most of fabrics is an almost periodic network of interlaced yarns or threads, whose periodicity is of the order of the terahertz wavelength. We report here on the diffraction of terahertz electromagnetic waves by the yarn network in common cloths. In the case of linen, this effect could lead to overestimating (by a factor as large as 3) the absorption when determined from the classical terahertz time-domain experiment. Our results are confirmed by a HFSS numerical simulation.