An apparatus for measurement control of a cell voltage of a fuel cell includes: terminals connected between the cells of a fuel cell connected in series; first resistors connected in series to the terminals; capacitors each connected in parallel between the first resistors to store voltages; switches connected to the first resistors to switch into a closed or an open state; a second resistor connected in series between a lowest cell among the cells and a semiconductor GND to provide a path for a current flow when an inverse voltage occurs in the cells; a diode connected in parallel to the second resistor to provide a path for a current flow when an inverse voltage does not occur in the cells; and a controller to change the state of each switch depending on a cell voltage measurement or open-wire diagnosis mode and perform cell voltage measurement and open-wire diagnosis.