Intermediate and massive stars drive fast and powerful isotropic winds that interact with the winds of nearby stars in star clusters and the surrounding interstellar medium (ISM). Wind-ISM collisions generate astrospheres around these stars that contain hotT similar to 10(7)K gas that adiabatically expands. As individual bubbles expand and collide they become unstable, potentially driving turbulence in star clusters. In this Letter we use hydrodynamic simulations to model a densely populated young star cluster within a homogeneous cloud to study stellar wind collisions with the surrounding ISM. We model a mass-segregated cluster of 20 B-type young main-sequence stars with masses ranging from 3 to 17M. We evolve the winds for similar to 11 kyr and show that wind-ISM collisions and overlapping wind-blown bubbles around B-stars mix the hot gas and ISM material, generating Kolmogorov-like turbulence on small scales early in its evolution. We discuss how turbulence driven by stellar winds may impact the subsequent generation of star formation in the cluster.