Context. Gaps in circumstellar disks can signal the existence of planetary perturbers, making such systems preferred targets for direct imaging observations of exoplanets. Aims. Being one of the brightest and closest stars to the Sun, the photometric standard star Vega hosts a two-belt debris disk structure. Together with the fact that its planetary system is being viewed nearly face-on, Vega has been one of the prime targets for planet imaging efforts. Methods. Using the vector vortex coronagraph on Keck/NIRC2 in the M_s band at 4.67 μm, we report the planet detection limits from 1 au to 22 au for Vega with an on-target time of 1.8 h. Results. We reach a 3 M_Jupiter limit outward of 12 au, which is nearly an order of magnitude deeper than for other existing studies. Combining our observations with existing radial velocity studies, we can confidently rule out the existence of companions more than ~8 M_Jupiter from 22 au down to 0.1 au for Vega. Interior and exterior to ~4 au, this combined approach reaches planet detection limits down to ~2–3 M_Jupiter using radial velocity and direct imaging, respectively. Conclusions. By reaching multi-Jupiter mass detection limits, our results are expected to be complemented by the planet imaging of Vega in the upcoming observations using the James Webb Space Telescope to obtain a more holistic understanding of the planetary system configuration around Vega.