The invention relates to a housing (10) for an electrical machine (50) and to an electrical machine (50) having such a housing (10). The housing (10) comprises an inner wall (12) and an outer wall (14), with a hollow space (16) therebetween for cooling the electrical machine (50) with a fluid. The housing (10) further has a sealing device (24, 26) on a front face (22, 23) of the housing (10). The housing is particularly characterised in that the sealing device (24, 26) comprises an annular sealing element (28) mounted between the inner wall (12) and the outer wall (14) so as to seal the front face, and in that the sealing device (24, 26) comprises a deflection ridge (30) which projects from the sealing element (28) in the axial direction of the housing (10) and is at least partially arranged between the walls (12, 14), the deflection ridge (30) being designed to lead a cooling fluid in the hollow space (16). A compact, economical and fluid-tight housing (10) can thus be advantageously provided.