The influence of Zn doping on the structural and magnetic properties of multiferroic BaMnF4 has been investigated using temperature dependent x-ray diffraction and magnetization measurements. With increasing Zn content the transition temperatures of the structural incommensurate phase transition as well as the AF ordering decrease. For x=0.75 no incommensurate phase is found anymore. The suppression of the structural transition can be explained due to the smaller size of Zn compared with Mn. The suppression of the antiferromagnetic ordering can be explained by a site dilution of the magnetic structure with nonmagnetic Zn. The percolation threshold is found to be xp =0.393 (4). This is in agreement with predictions for a site-diluted square-lattice weak-anisotropy two-dimensional Heisenberg antiferromagnet with S= 5 2.