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 \pm 3 km s ^ { -1 } , in good agreement with measurements based on the [ \ion Cii ] and H \alpha + [ \ion Nii ] lines , and a velocity dispersion of \sigma = 27 \pm 3 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 .