A battery system includes: a battery pack including a battery housing and a plurality of battery cells accommodated within the battery housing; and a cover element covering an outer side of the battery housing. The battery housing has a housing exit at where a venting gas stream exhausted by one or more of the battery cells during a thermal runaway exits the battery housing, and the cover element covers the housing exit. The cover element forms a venting channel together with the outer side of the battery housing such that the venting gas stream exiting the housing exit is received and guided by the venting channel along the outer side of the battery housing to a channel exit of the venting channel.