The line-of-sight velocities and [O III] 5007 Å expansion velocities are measured for 11 planetary nebulae (PNs) in the Virgo Cluster core, at 15 Mpc distance, with the FLAMES spectrograph on the ESO VLT. These PNs are located about halfway between the two giant elliptical galaxies M87 and M86. From the [O III] 5007 Å line profile widths, the average half-width at half-maximum expansion velocity for this sample of 11 PNs is v¯HWHM=16.5 km s-1 (rms=2.6 km s-1). We use the PN subsample bound to M87 to remove the distance uncertainties and the resulting [O III] 5007 Å luminosities to derive the central star masses. We find these masses to be at least 0.6 Msolar and obtain PN observable lifetimes tPN<2000 yr, which imply that the bright PNs detected in the Virgo Cluster core are compact, high-density nebulae. We finally discuss several scenarios for explaining the high central star masses in these bright M87 halo PNs.