The discovery of superconductivity in Nd_0.8Sr_0.2NiO₂ introduced a new family of layered nickelate superconductors that has now been extended to include a range of strontium doping, praseodymium or lanthanum in place of neodymium, and the five-layer compound Nd₆Ni₅O₁₂. A number of studies have indicated that electron correlations are strong in these materials, a feature that often leads to the emergence of magnetism. Here we report muon spin rotation/relaxation studies of a series of superconducting infinite-layer nickelates. Regardless of the rare earth ion or doping, we observe an intrinsic magnetic ground state arising from local moments on the nickel sublattice. The coexistence of magnetism - which is likely to be antiferromagnetic and short-range ordered - with superconductivity is reminiscent of some iron pnictides and heavy fermion compounds, and qualitatively distinct from the doped cuprates.