Optoacoustic signals are typically reconstructed into images using inversion algorithms applied in the time-domain. However, time-domain reconstructions can be computationally intensive and therefore slow when large amounts of raw data are collected from an optoacoustic scan. Here we considered a fast weighted ω-k (FWOK) algorithm operating in the frequency domain to accelerate the inversion in raster-scan optoacoustic mesoscopy (RSOM), while seamlessly incorporating impulse response correction with minimum computational burden. We investigated the FWOK performance with RSOM measurements from phantoms and mice in vivo and obtained 360-fold speed improvement over inversions based on the back-projection algorithm in the time-domain. This previously unexplored inversion of in vivo optoacoustic data with impulse response correction in frequency domain reconstructions points to a promising strategy of accelerating optoacoustic imaging computations, toward video-rate tomography.