We report results of a muon spin rotation (µSR) study of the cuprate-analog nickelate La4Ni3O8, which undergoes a transition at 105 K to a low-temperature phase with charge-stripe and antiferromagnetic (AFM) order on square planar NiO2 layers. Zero-field µSR shows that the AFM transition is abrupt, commensurate and has a quasi-2D character below ∼25 K. Comparison of observed muon precession frequencies with Ni dipolar field calculations yields Ni moments 0.5µB . Dynamic muon spin relaxation above 105 K suggests critical slowing of Ni spin fluctuations, but is inconsistent with corresponding 139 La NMR results. Critical slowing and an abrupt transition are also observed in the planar cuprate AFM La2CuO 4+δ , where they are taken as evidence for weakly interplanar-coupled two-dimensional AFM spin fluctuations, but our µSR data do not agree quantitatively with theoretical predictions for this scenario when applied to the nickelate.