Vertical-external-cavity surface-emitting semiconductor lasers (VECSELs) are of increasing interest for applications requiring ultra-coherence and/or low noise at novel wavelengths; performance that is currently achieved via high-Q, air-spaced resonators to achieve long intra-cavity photon lifetimes (for the so-called class-A low noise regime), power scaling and high beam quality. Here, we report on the development of a compact, electronically tunable, monolithic-cavity, class-A VECSEL (monolithic VECSEL) for ultra-narrow free-running linewidths. A multi-quantum-well, resonant periodic gain structure with integrated distributed Bragg reflector (DBR) was optically-bonded to an air-gap-free laser resonator created inside a right-angle fused-silica prism to suppress the influence of environmental noise on the external laser oscillation, thus achieving high stability. Mode-hop-free wavelength tuning is performed via the stabilized temperature; or electronically, and with low latency, via a shear piezo-electric transducer mounted on the top of the prism. The free-running linewidth, estimated via the frequency power spectral density (PSD), is sub-kHz over ms timescales and <1.9 kHz for time sampling as long as 1s, demonstrating at least two orders-of-magnitude improvement in noise performance compared to previously reported single frequency VECSELs. The stable, total internal reflection resonator concept is akin to the prevalent monolithic non-planar ring oscillator (NPRO), however the monolithic VECSEL has several important advantages: tailored emission wavelength (via semiconductor bandgap engineering), no relaxation oscillations, no applied magnetic field, and low requirements on the pump beam quality. This approach is power-scalable in principle and could be applied to VECSELs at any of the wavelengths from the visible to the mid-infrared at which they are already available, to create a range of robust, ultra-coherent laser systems with reduced bulkiness and complexity. This is of particular interest for remote metrology and the translation of quantum technologies, such as optical clocks, from research laboratories into real world applications.