Using muon-spin rotation, we studied the in-plane (lambda_{ab}) and the out of plane (lambda_{c}) magnetic field penetration depth in SrFe_{1.75}Co_{0.25}As_{2} (T_{c} approximately 13.3 K). The penetration depth anisotropy gamma_{lambda} = lambda_{c}/lambda_{ab} increases from gamma_{lambda} approximately 2.1 at T_{c} to 2.7 at 1.6 K. The mean internal field in the superconducting state increases with decreasing temperature, just opposite to the diamagnetic response seen in magnetization experiments. This unusual behavior suggests that the external field induces a magnetic order which is maintained throughout the whole sample volume.