The work was carried out by Watson Property Management, the contractor which maintains the block of flats where the tree stands in Chorlton.
Local councillor Paul Ankers said: 'It is important to enforce tree preservation orders and this was a particularly important tree. Chorlton is seen as a leafy area but this street doesn't have many leafy trees.'
He confirmed the council was considering launching legal proceedings against Watson Property Management.
Tim Mullen, from Watson Property Management, in Wetherby, West Yorkshire, said he knew nothing about the tree and had not been contacted by the council.