We have measured the sideward flow of neutral strange ($K^0_s$) mesons in 6 AGeV Au + Au collisions. A prominent anti-flow signal is observed for an impact parameter range (b $lesssim 7$ fm) which spans central and mid-central events. Since the $K^0_s$ scattering cross section is relatively small in nuclear matter, this observation suggests that the in-medium kaon vector potential plays an important role in high density nuclear matter.