For systems with only finite-range interactions between different sites Lieb and Robinson have shown that there is an upper bound for the velocity of a perturbation spreading through the system, the so-called Lieb-Robinson bound. The Lieb-Robinson bound causes a light cone, i.e. a local perturbation does not reach distant sites of the lattice instaneously, so that for sufficiently small times distant sites of the system have not noticed the local perturbation yet. The velocity of the perturbation depends on the model and the parameters of its Hamiltonian. Besides in higher dimensions it is important to answer the question how the perturbation propagates through the system, i.e. whether it respects the lattice structure (Manhattan metric) or if the system behaves like a continuum (Euclidian metric). We compute the time evolution of a local perturbation given by a single spin down for the two-dimensional transverse-field Ising model with nearest-neighbour interactions on the square lattice. Using a time-dependent application of mean-field theory based on the BBGKY hierarchy we are able to study the system deep in the ferromagnetic for values of the transverse field up to 0.6 on a lattice of the size 101x101. We find that at short distances the propagation of the perturbation obeys the Manhattan metric, while at larger distances the system more and more behaves like a continuum and the propagation of the perturbation can be described with the Euclidian metric. In contrast to the one-dimensional transverse-field Ising model, for which the velocity increases linearly with the transverse field, we find a quadratic dependence of the velocity on the transverse field.