Multipliers are operators which have important applications for signal processing and acoustics. Also, woven and weaving Bessel sequences and frames are very important and practical tools in the applications of frames. In this study, we define the notion of multiplier for woven and weaving frames and we show that the properties of multiplier continuously depend on the chosen symbol sequence m and two chosen woven Bessel sequences. Further, we study the stability of woven frames under perturbation and its connection with multipliers.