A microwave generator having a central electrode (14) which at the front end has a radiating element (22) and an external electrode (18) which coaxially surrounds the central electrode (14) along an axially extending resonator portion (16), wherein the two electrodes (14 and 18) are of a rotationally symmetrical configuration and define a spark gap (62) which sparks across when a high voltage is applied and radiates microwaves by way of the resonator portion (16) and the radiating element (22) of the central electrode (14). The spark gap (62) is in the form of an annular spark gap, which is determined by a connection element (26) which projects at the rear end axially centrally away from the central electrode (14) and an annular edge (44) of the external electrode (18), the edge being provided coaxially with respect to the connection element (26). The central electrode (14) and the external electrode (18) are arranged in a housing sleeve (12) of an electrically insulating material. The housing sleeve (12) preferably has an extension (58) defining a space (56) in which there is arranged a high voltage source (30), which is electrically conductively connected to the electrodes (14 and 18) of the microwave generator (10).