The invention relates to a battery system, in particular for a hybrid drive, having a housing, a plurality of battery cells arranged inside the housing and a cooling element, wherein fluid connections and at least one electrical connection are arranged on the housing, said electrical connection being electrically coupled to the battery cells, and wherein the fluid connections comprise at least one coolant inlet and at least one coolant outlet, each of which is fluidically connected to the cooling element. The invention is characterized in that the housing comprises a tubular main body, which is sealed in a fluid-tight manner by a closure cap at each of the opposite end faces thereof, wherein the electrical connection is arranged on a first closure cap and the fluid connections are arranged on a second closure cap. The invention also relates to a motor vehicle having such a battery system.