  We consider a scenario in which Sgr A* is in a massive black hole binary
(MBHB) with an as-of-yet undetected supermassive or intermediate-mass black
hole companion. Dynamical encounters between this MBHB and single stars in its
immediate vicinity would eject hypervelocity stars (HVSs) with velocities
beyond the Galactic escape velocity. In this work, we use existing HVS
observations to constrain for the first time the existence of a companion to
Sgr A*. We simulate the ejection of HVSs via the `MBHB slingshot' scenario and
show that the population of HVSs detectable today depends strongly on the
companion mass and the separation of the MBHB. We demonstrate that the lack of
uncontroversial HVS candidates in \textit{Gaia} Data Release 3 places a firm
upper limit on the mass of a possible Sgr A* companion. Within one milliparsec
of Sgr A*, our results exclude a companion more massive than $1000 \,
\mathrm{M_\odot}$. If Sgr A* recently merged with a companion black hole, our
findings indicate that unless this companion was less massive than $500 \,
\mathrm{M_\odot}$, this merger must have occurred at least $10$ Myr ago. These
results complement and improve upon existing independent constraints on a
companion to Sgr A* and show that large regions of its parameter space can now
be ruled out.
