  We present the results from ALMA observations centred $40^{\prime\prime}$ (3
kpc in projection) southeast of the nucleus of M87. We report the detection of
extended CO (2-1) line emission with a total flux of $(5.5 \pm 0.6) \times
10^{-18}$ erg s$^{-1}$ cm$^{-2}$ and corresponding molecular gas mass
$M_{H_2}=(4.7 \pm 0.4) \times 10^5 M_\odot$, assuming a Galactic CO to H$_2$
conversion factor. ALMA data indicate a line-of-sight velocity of $-129\pm3$ km
s$^{-1}$, in good agreement with measurements based on the [CII] and
H$\alpha$+[NII] lines, and a velocity dispersion of $\sigma=27\pm3$ km
s$^{-1}$. The CO(2-1) emission originates only outside the radio lobe of the
AGN seen in the 6~cm VLA image, while the filament prolongs further inwards at
other wavelengths. The molecular gas in M87 appears to be destroyed or excited
by AGN activity, either by direct interaction with the radio plasma, or by the
shock driven by the lobe into the X-ray emitting atmosphere. This is an
important piece of the puzzle in understanding the impact of the central AGN on
the amount of the coldest gas from which star formation can proceed.
