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The features of pulsed $\gamma$-ray emission from classical and millisecondpulsars indicate that the high energy radiation processes in their innermagnetospheres occur in a similar way. In the last decade several TeV$\gamma$-ray nebulae have been discovered around classical pulsars. The abovefacts suggest that $\gamma$-rays should be produced also in the surroundings ofmillisecond pulsars. We discuss a model for the bow shock nebula around thewell known Black Widow binary system containing the millisecond pulsarB1957+20. This model predicts the existence of a synchrotron X-ray and inverseCompton $\gamma$-ray nebula around this system. We want to find out whether$\gamma$-ray emission from the nebula around B1957+20 could be detected by thefuture and present Cherenkov telescopes. Using the Monte Carlo method wefollowed the propagation of relativistic electrons in the vicinity of thepulsar. We calculated the very high energy radiation produced by them in thesynchrotron process and the inverse Compton scattering of the MicrowaveBackground Radiation and of the infrared radiation from the galactic disk. Wealso computed the X-ray emission produced by the electrons in the synchrotronprocess. We show that the hard X-ray tail emission observed from the vicinityof B1957+20 can be explained by our model. Moreover, we predict that the TeV$\gamma$-ray emission produced by the electrons in the inverse Compton processshould be detectable by the future Cherenkov Telescope Array and possibly bythe long term observations with the present Cherenkov arrays such as MAGIC andVERITAS. The $\gamma$-ray emission from B1957+20 is expected to be extended,inhomogeneous, and shifted from the present location of the binary system by adistance comparable to the radius of the nebula.

High energy emission from the nebula around the Black Widow binary system containing millisecond pulsar B1957+20