The Martian ionosphere, modulated by the solar wind from the topside and remnant crustal magnetic fields close to the surface, possesses unique structures different from Earth and Venus. Integrated observations by the plasma and magnetic field instruments onboard the Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft show evidence of ionospheric plasma depletions, independent of seasonal variations at Mars. During such depletions, the density of all ionospheric ion species is reduced by more than an order of magnitude, and, at the same time, the electron temperature increases abruptly. An automated algorithm for the identification of such plasma depletions is developed. Altogether, as many as 1177 events are identified in 8618 orbits available from October 2014 to May 2021. A statistical investigation of these events reveals that they are more prominent on the nightside. Their higher occurrence in the southern hemisphere suggests a possible relation to the crustal magnetic fields. While the dayside events occur mainly at altitudes above about 200 km, nightside event altitudes are typically lower. Considering the relation between spacecraft velocity and observed event duration, we suggest that the depletions are bubble-like structures, more elongated horizontally than vertically. A possible mechanism of their formation is discussed.