Using muon-spin rotation, we studied the in-plane (lambda_ab) and the out of plane (lambda_c) magnetic field penetration depth in SrFe_1.75Co_0.25As_2 (T_c=13.3 K). Both lambda_ab(T) and lambda_c(T) are consistent with the presence of two superconducting gaps with the gap to T_c ratios 2Delta/k_BT_c=7.2 and 2.7. The penetration depth anisotropy gamma_lambda=lambda_c/lambda_ab increases from gamma_lambda=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.
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