Using pump-probe optical polarimetry we demonstrate that femtosecond laser excitation of a 2D regular lattice of magnetic nanodots effectively changes the optical anisotropy of the array. Study of the dynamics of the femtosecond laser-induced anisotropy reveals four main mechanisms occurring in the electronic, spin, and lattice subsystems. Below 1 ps, a strong Kerr-like nonlinearity causes linear birefringence, with its axis directed along the electric field of the linearly polarized femtosecond laser pump pulse. In addition, a long-living linear birefringence is also induced due to slowly relaxing excitations. Also below 1 ps, ultrafast laser-induced demagnetization of Co leads to a partial breakdown of the circular birefringence of the magnetic nanodots. On the timescale up to 300 ps, optically triggered acoustic modes of the dots drive oscillations of the linear optical birefringence. During this process, the oscillations damp while transferring their energy into acoustic modes of the substrate. On the nanosecond timescale, the signal is dominated by acoustic oscillations at the surface of the substrate.