A microphone package wherein an MEMS microphone chip (MIC) is mounted on a substrate (SUB) and is sealed with a cover (ABD) with respect to the substrate. The membrane (MMB) of the microphone chip is connected to a sound entry opening (SEO) in the substrate via an acoustic channel. As a result of defined dimensioning of, in particular, the cross section and length of sound entry opening and channel, an acoustic low-pass filter is formed, the −3 dB attenuation point of which is significantly below the natural resonance of microphone membrane and package.