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We report the experimental observation of the polarization modulation instability (PMI) effect in all-normal dispersion (ANDi) microstructured optical fibers (MOFs) with quasi-continuous pumping. The small unintentional birefringence (~10^-5), that any realistic non-polarization maintaining MOF exhibits, contributes to this nonlinear effect. PMI can produce two sidebands whose polarization state is orthogonal to the polarization of the pump. In this work, only one type of PMI process is observed, i.e., when the pump is polarized along the slow axis of the fiber and sidebands are generated in the fast axis mode. This PMI process was studied experimentally in two ANDi fibers with different dispersion features and pumped with long (700 ps) pump pulses at 1064 nm. Experimental results are compared with theoretical calculations, with reasonably good agreement.