We propose a scheme for the emission of few-cycle dispersive waves in the mid-infrared using hollow-core photonic crystal fibers filled with noble gas. The underlying mechanism is the formation of a plasma cloud by a self-compressed, sub-cycle pump pulse. The resulting free-electron population modifies the fiber dispersion, allowing phase-matched access to dispersive waves at otherwise inaccessible frequencies, well into the mid-IR. Remarkably, the pulses generated turn out to have durations of the order of two optical cycles. In addition, this ultrafast emission, which occurs even in the absence of a zero dispersion point between pump and mid-IR wavelengths, is tunable over a wide frequency range simply by adjusting the gas pressure. These theoretical results pave the way to a new generation of compact, fiber-based sources of few-cycle mid-IR radiation.