Inclusive and semi-inclusive measurements are presented for antiproton ($bar{p}$) production in proton-nucleus collisions at the AGS. The inclusive yields per event increase strongly with increasing beam energy and decrease slightly with increasing target mass. The $bar{p}$ yield in 17.5 GeV/c p+Au collisions decreases with grey track multiplicity, $N_g$, for $N_g>0$, consistent with annihilation within the target nucleus. The relationship between $N_g$ and the number of scatterings of the proton in the nucleus is used to estimate the $bar{p}$ annihilation cross section in the nuclear medium. The resulting cross section is at least a factor of five smaller than the free $bar{p}-p$ annihilation cross section when assuming a small or negligible formation time. Only with a long formation time can the data be described with the free $bar{p}-p$ annihilation cross section.