We describe a monolithic approach to fabricating large-scale arrays of high-finesse and low-mode-volume Fabry-Perot microcavities with open access to the air core. A stress-driven buckling self-assembly technique was used to form half-symmetric curved-mirror cavities, and a dry etching process was subsequently used to create micropores through the upper mirror. We show that the cavities retain excellent optical properties, with reflectance-limited finesse ∼2500 and highly predictable Laguerre-Gaussian modes. We furthermore demonstrate the ability to introduce liquids into the cavity region by microinjection through the pores. Applications in sensing, optofluidics, and cavity quantum electrodynamics are envisioned.