Light-matter interactions in optical cavities underpin many applications of integrated quantum photonics. Among various solid-state platforms, hexagonal boron nitride (hBN) is gaining considerable interest as a compelling van der Waals host of quantum emitters. However, progress to date has been limited by an inability to engineer simultaneously an hBN emitter and a narrow-band photonic resonator at a predetermined wavelength. Here, we overcome this problem and demonstrate deterministic fabrication of hBN nanobeam photonic crystal cavities with high quality factors over a broad spectral range (∼400 to 850 nm). We then fabricate a monolithic, coupled cavity-emitter system designed for a blue quantum emitter that has an emission wavelength of 436 nm and is induced deterministically by electron beam irradiation of the cavity hotspot. Our work constitutes a promising path to scalable on-chip quantum photonics and paves the way to quantum networks based on van der Waals materials.