We present surface photometry and stellar kinematics of NGC 4264, a barred lenticular galaxy in the region of the Virgo Cluster undergoing a tidal interaction with one of its neighbours, NGC 4261. We measured the bar radius (abar = 3.2 ± 0.5 kpc) and strength (Sbar = 0.31 ± 0.04) of NGC 4264 from Sloan Digital Sky Survey imaging and its bar pattern speed (Ωbar = 71 ± 4 km s-1 kpc-1) using the Tremaine-Weinberg method with stellar-absorption integral-field spectroscopy performed with the Multi Unit Spectroscopic Explorer at the Very Large Telescope. We derived the circular velocity (Vcirc = 189 ± 10 km s-1) by correcting the stellar streaming velocity for asymmetric drift and calculated the corotation radius (Rcor = 2.8 ± 0.2 kpc) from the bar pattern speed. Finally, we estimated the bar rotation rate (Rcor/abar = 0.88 ± 0.23). We find that NGC 4264 hosts a strong and large bar extending out to the corotation radius. This means that the bar is rotating as fast as it can like nearly all the other bars measured so far even when the systematic error due to the uncertainty on the disc position angle is taken into account. The accurate measurement of the bar rotation rate allows us to infer that the formation of the bar of NGC 4264 was due to self-generated internal processes and not triggered by the ongoing interaction.