The behaviour near the initial state of the anisotropy parameter of the arbitrary type, homogeneous and anisotropic Bianchi models is considered in the framework of the braneworld cosmological models. The matter content on the brane is assumed to be an isotropic perfect cosmological fluid obeying a barotropic equation of state. To obtain the value of the anisotropy parameter at an arbitrary moment an evolution equation is derived, describing the dynamics of the anisotropy as a function of the volume scale factor of the universe. The general solution of this equation can be obtained in an exact analytical form for the Bianchi I and V types and in a closed form for all other homogeneous and anisotropic geometries. The study of the values of the anisotropy in the limit of small times shows that for all Bianchi-type spacetimes filled with a non-zero pressure cosmological fluid, obeying a linear barotropic equation of state, the initial singular state on the brane is isotropic. This result is obtained by assuming that in the limit of small times the asymptotic behaviour of the scale factors is of Kasner-type. For braneworlds filled with dust, the initial values of the anisotropy coincide in both braneworld and standard four-dimensional general relativistic cosmologies.