Portable mid-infrared (mid-IR) spectroscopy and sensing applications require widely tunable, narrow linewidth, chip-scale, single-mode sources without sacrificing significant output power. However, no such lasers have been demonstrated beyond 3 $mu$m due to the challenge of building tunable, high quality-factor (Q) on-chip cavities. We demonstrate a tunable, single-mode mid-IR laser at 3.4 $mu$m using a high-Q silicon microring cavity with integrated heaters and a multi-mode Interband Cascade Laser (ICL). We show that the multiple longitudinal modes of an ICL collapse into a single frequency via self-injection locking with an output power of 0.4 mW and achieve an oxide-clad high confinement waveguide microresonator with a loaded Q of $2.8times 10^5$. Using integrated microheaters, our laser exhibits a wide tuning range of 54 nm at 3.4 $mu$m with 3 dB output power variation. We further measure an upper-bound effective linewidth of 9.1 MHz from the locked laser using a scanning Fabry-Perot interferometer. Our design of a single-mode laser based on a tunable high-Q microresonator can be expanded to quantum-cascade lasers at higher wavelengths and lead to the development of compact, portable, high-performance mid-IR sensors for spectroscopic and sensing applications.