In this paper, we have studied the three-dimensional (3D) electron-acoustic waves (EAWs) in a three component complex plasma containing $q$-non-extensive distributed hot electrons and positrons. The propagation characteristics of the 3D electron-acoustic (EA) shock waves under the influence of magnetic field have been studied. Our present plasma model supports the negative potential shocks. Combined action of dissipation ($\eta$), nonextensivity ($q$), concentration of positrons ($\beta$), temperature ratio of cold electrons to positrons ($\sigma$) and magnetic field ($\omega_{c}$) on the EA shock waves has been studied in detail and the findings obtained here will be beneficial in future astrophysical investigations.