Compressible low-Reynolds-number flow over a square cylinder was investigated using a low-density wind tunnel. The Reynolds number based on the height of the square cylinder, $Re$, was set to between 1000 and 5000 and the freestream Mach number, $M$, was set to between 0.1 and 0.7. Flow visualization using a Schlieren optical system and pressure-sensitive paint was conducted along with steady aerodynamic force and unsteady pressure measurements. Schlieren visualization at $Re=2000$ captured a drastic change in the flow pattern at high Mach numbers ($M\ge 0.65$). The steady region of the separated shear layer and the recirculation region rapidly expanded downstream at high Mach numbers. The drag coefficient, $C_D$, increases as the Mach number increases up to $M\le 0.6$, and then decreases for $M>0.6$. There is thus a sharp peak in the $M$–$C_D$ curve. The Mach number corresponding to this peak at $Re=2000$ was identified as $M\approx 0.6$. The back pressure also rapidly decreases and increases at around $M=0.6$, and thus, the rapid increase and decrease in the drag coefficient is due to the change in the back pressure caused by the reduced and expanded recirculation region. In addition, pressure-sensitive paint measurements revealed that the pressure coefficient on the side surface of the square cylinder increases with increasing the Mach number and that the location of maximum pressure changes with the Mach number. This change is related to the change in the recirculation region.