The analytical solution of the scalar two-dimensional problem of TM-wave diffraction by a single subwavelength slit perforated in a thick perfectly conducting screen and filled with a metamaterial is obtained. The phenomenon of extraordinary transmission through the slit filled with the epsilon-negative or double-negative media is discovered. The dependence of the slit transmittance on the problem parameters is presented. The analysis of the slit electromagnetic response clearly reveals the unity of physical nature of the conventional Fabry-Perot resonances and the extraordinary transmission peak emerged in the evanescent-mode regime of the slit. It is shown that the negative plasma-like frequency-dependent dielectric acts as a qualitative model of the dispersive properties of the below-cutoff holes perforated in a screen. The results of the physical analysis of diffraction by the two-dimensional geometry under study are generalized to the case of three-dimensional hole structures.