The giant radio galaxy M87 with its proximity (16Mpc), famous jet, and very massive black hole ((3 - 6) × 109M·) provides a unique opportunity to investigate the origin of very high energy (VHE; E > 100GeV) γ-ray emission generated in relativistic outflows and the surroundings of supermassive black holes. M87 has been established as a VHE γ-ray emitter since 2006. The VHE γ-ray emission displays strong variability on timescales as short as a day. In this paper, results from a joint VHE monitoring campaign on M87 by the MAGIC and VERITAS instruments in 2010 are reported. During the campaign, a flare at VHE was detected triggering further observations at VHE (H.E.S.S.), X-rays (Chandra), and radio (43GHz Very Long Baseline Array, VLBA). The excellent sampling of the VHE γ-ray light curve enables one to derive a precise temporal characterization of the flare: the single, isolated flare is well described by a two-sided exponential function with significantly different flux rise and decay times of τrised = (1.69 ± 0.30) days and τdecayd = (0.611 0.080) days, respectively. While the overall variability pattern of the 2010 flare appears somewhat different from that of previous VHE flares in 2005 and 2008, they share very similar timescales (day), peak fluxes (Φ>0.35 TeV ≃ (1-3) × 10-11 photonscm-2 s-1), and VHE spectra. VLBA radio observations of 43GHz of the inner jet regions indicate no enhanced flux in 2010 in contrast to observations in 2008, where an increase of the radio flux of the innermost core regions coincided with a VHE flare. On the other hand, Chandra X-ray observations taken 3 days after the peak of the VHE γ-ray emission reveal an enhanced flux from the core (flux increased by factor 2; variability timescale