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M87 has recently been shown to be a TeV source that is likely to be variable. Based on this and on contemporaneous optical and X-ray monitoring, we argue that the source of the TeV emission is the core of M87 and not one of two jet knots (HST-1 and A), with an X-ray brightness comparable to that of the core. We model the TeV emission in the core as inverse Compton (IC) emission from the base of the jet. Homogeneous models fail to reproduce the spectral energy distribution (SED) and, in particular, the TeV flux. They also fail to comply with the unified scheme of BL Lacertae (BL) objects and FR I radio galaxies. A jet that decelerates from a Lorentz factor Γ~ 20 down to Γ~ 5 over a length of~ 0.1 pc reproduces the observed SED of the M87 core and, when aligned with the line of sight, produces a SED similar to those of TeV BLs. The TeV flux in the decelerating jet model is successfully reproduced as upstream …