An indirect measurement of the antiproton flux in cosmic rays is possible as the particles undergo deflection by the geomagnetic field. This effect can be measured by studying the deficit in the flux, or shadow, created by the Moon as it absorbs cosmic rays that are headed towards the Earth. The shadow is displaced from the actual position of the Moon due to geomagnetic deflection, which is a function of the energy and charge of the cosmic rays. The displacement provides a natural tool for momentum/charge discrimination that can be used to study the composition of cosmic rays. Using 33 months of data comprising more than 80 billion cosmic rays measured by the High Altitude Water Cherenkov (HAWC) observatory, we have analyzed the Moon shadow to search for TeV antiprotons in cosmic rays. We present our first upper limits on the $bar{p}/p$ fraction, which in the absence of any direct measurements, provide the tightest available constraints of $sim1%$ on the antiproton fraction for energies between 1 and 10 TeV.