A lubricant cartridge container which supplies a fluid lubricant to a lubricating pump by being attached to a connecting member of the lubricating pump provided with a lubricant inflow portion for leading the fluid lubricant to the lubricating pump, the lubricant cartridge container comprising: a cylindrical member configured to be able to fill the fluid lubricant therein, attached to the connecting member of the lubricating pump, and supplying the fluid lubricant to the lubricating pump through the lubricant inflow portion when subjected to a suction force from the lubricating pump side; and a moving member disposed inside the cylindrical member so as to accommodate the fluid lubricant in a space portion formed between the moving member and the lubricant inflow portion in a state where the cylindrical member is attached to the connecting member of the lubricating pump, and moving inside the cylindrical member toward the lubricant inflow portion side as the fluid lubricant flows toward the lubricant inflow portion side when subjected to the suction force from the lubricating pump side, wherein: the cylindrical member has a shoulder portion positioned on a lateral surface side of the lubricant inflow portion when the cylindrical member is attached to the connecting member of the lubricating pump; the moving member has a first moving main body portion capable of moving inside the cylindrical member and coming in contact with the shoulder portion, and a second moving main body portion capable of coming in contact with the lubricant inflow portion after the first moving main body portion comes in contact with the shoulder portion; the second moving main body portion has a center portion (26C1) capable of coming in contact with the lubricant inflow portion, and a step portion (26C2) connecting the center portion (26C1) and the first moving main body portion; and the center portion (26C1) has a recess recessed in a polygonal shape formed by connecting a plurality of apexes in a plan view in order to facilitate deformation or displacement at the center portion (26C1) and the step portion (26C2) when subjected to the suction force. a cylindrical member configured to be able to fill the fluid lubricant therein, attached to the connecting member of the lubricating pump, and supplying the fluid lubricant to the lubricating pump through the lubricant inflow portion when subjected to a suction force from the lubricating pump side; and a moving member disposed inside the cylindrical member so as to accommodate the fluid lubricant in a space portion formed between the moving member and the lubricant inflow portion in a state where the cylindrical member is attached to the connecting member of the lubricating pump, and moving inside the cylindrical member toward the lubricant inflow portion side as the fluid lubricant flows toward the lubricant inflow portion side when subjected to the suction force from the lubricating pump side, wherein: the cylindrical member has a shoulder portion positioned on a lateral surface side of the lubricant inflow portion when the cylindrical member is attached to the connecting member of the lubricating pump; the moving member has a first moving main body portion capable of moving inside the cylindrical member and coming in contact with the shoulder portion, and a second moving main body portion capable of coming in contact with the lubricant inflow portion after the first moving main body portion comes in contact with the shoulder portion; the second moving main body portion has a center portion (26C1) capable of coming in contact with the lubricant inflow portion, and a step portion (26C2) connecting the center portion (26C1) and the first moving main body portion; and the center portion (26C1) has a recess recessed in a polygonal shape formed by connecting a plurality of apexes in a plan view in order to facilitate deformation or displacement at the center portion (26C1) and the step portion (26C2) when subjected to the suction force. the cylindrical member has a shoulder portion positioned on a lateral surface side of the lubricant inflow portion when the cylindrical member is attached to the connecting member of the lubricating pump; the moving member has a first moving main body portion capable of moving inside the cylindrical member and coming in contact with the shoulder portion, and a second moving main body portion capable of coming in contact with the lubricant inflow portion after the first moving main body portion comes in contact with the shoulder portion; the second moving main body portion has a center portion (26C1) capable of coming in contact with the lubricant inflow portion, and a step portion (26C2) connecting the center portion (26C1) and the first moving main body portion; and the center portion (26C1) has a recess recessed in a polygonal shape formed by connecting a plurality of apexes in a plan view in order to facilitate deformation or displacement at the center portion (26C1) and the step portion (26C2) when subjected to the suction force.