Many researchers have reported that inter-yarn friction has an important effect on the response of the plain-weave fabric to an impact. However, the effects of inter-yarn friction on impact responses of woven fabrics with other weaves have not been studied in detail. In the present work, numerical analysis was utilized to study the effects of inter-yarn friction on responses of woven fabrics with different weaves (the plain weave, 2/2 twill, 2/2 basket, and 3/1 twill) to a low-velocity impact. Both inter-yarn friction and the weaves of the woven fabrics greatly influenced the responses of the fabrics to a low-velocity impact. The higher the inter-yarn friction, the higher the levels of the tensile stresses concentrated near the centers of impact of the woven fabrics, and the earlier the failures of the fabrics. In addition, the greater the inter-yarn friction, the higher the velocities of the transverse stress waves in the woven fabrics, and the more effective the distributions of impact energy from the primary yarns of the fabrics to the secondary yarns of the fabrics. Although it had the lowest velocity of the transverse stress wave, due to its firmly interlaced yarns, the plain-weave fabric had the highest total energy absorption capacity among the woven fabrics with the different weaves. On the other hand, due to its loosely interlaced yarns, the 3/1 twill fabric had the lowest total energy absorption capacity among the woven fabrics.