We consider vector valued weak solutions \(u:\Omega _T\rightarrow \mathbb {R}^N\) with \(N\in \mathbb {N}\) of degenerate or singular parabolic systems of type \(\begin{aligned} \partial _t u - \textrm{div} \, a(z,u,Du) = 0 \qquad \text {in}\qquad \Omega _T= \Omega \times (0,T), \end{aligned}\) where \(\Omega \) is an open set in \(\mathbb {R}^{n}\) for \(n\ge 1\) and \(T>0\) denotes a finite time. Assuming that the vector field a is not of Uhlenbeck-type structure, is continuous with respect to the solution variable u and satisfies a VMO-condition in the space-time variable z, we show that the solution u is partially Hölder continuous for every exponent \(\alpha \in (0,1)\) , provided the vector field degenerates like that of the p-Laplacian for small gradients.