A battery cell for a battery of a motor vehicle with a battery cell housing in which is accommodated a galvanic element. The battery cell has two electric connections by means of which the battery cell can be electrically connected to at least one other battery cell of the battery. At least one switching element can be transferred by means of a control unit into a switching state in which an electrically conductive connection between an arrester of the galvanic element and of at least one of the electric connections is interrupted. In addition, the invention relates to a battery with a plurality of such battery cells as well as to a motor vehicle with a battery.