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Materials with strongly correlated electrons often exhibit interesting physical properties. An example of these materials is the layered oxide perovskite Sr2RuO4, which has been intensively investigated due to its unusual properties. Whilst the debate on the symmetry of the superconducting state in Sr2RuO4 is still ongoing, a deeper understanding of the Sr2RuO4 normal state appears crucial as this is the background in which electron pairing occurs. Here, by using low-energy muon spin spectroscopy we discover the existence of surface magnetism in Sr2RuO4 in its normal state. We detect static weak dipolar fields yet manifesting at an onset temperature higher than 50 K. We ascribe this unconventional magnetism to orbital loop currents forming at the reconstructed Sr2RuO4 surface. Our observations set a reference for the discovery of the same magnetic phase in other materials and unveil an electronic ordering mechanism that can influence electron pairing with broken time reversal symmetry.