According to the recent Gramophone Feature's article on Mozart:
Mozart's burial outside the city in a communal grave was in accordance with the prevalent custom of the time, influenced by Emperor Joseph II's reforms, proposed in 1784, encouraging simple, economical and hygienic burials.
Many go even further and believe that Mozart was given a "pauper's burial" and that he was sewn naked into a linen sheet and crudely ejected into mass grave from a re-usable coffin. The bottom doors swing open: the pauperized genius lands with a thump in the open pit.
But none of this is true. Or it probably isn't true. Recent research strongly suggests that Mozart was buried in an individual grave and in an ordinary coffin. The widespread belief in a "simple" burial, and a mass or communal grave, is based on a number of assumptions which simply do not stand up to scrutiny.
The first major assumption is the idea, repeated by Gramophone, that Mozart's burial took place in accordance with the Emperor Joseph II's reforms. But the truth was that these reforms didn't actually make it into law. The Emperor did indeed propose to make mass graves and linen sacks compulsory, but the outcry from the citizenry was so widespread and so vociferous, the bulk of the proposals never made it into law. In fact, the Emperor released a statement in which he officially retracted the offending proposals.
Judging from the violence of the opposition to Emperor's proposals and from documentary evidence of various kinds (including detailed financial statements itemising the funeral expenses of Mozart's friends), the common practice seems to be much what we now think of a standard burial: an individual plot, an individual coffin, the corpse fully clothed. Words, music, tears. That is almost certainly what happened in Mozart's case.
Furthermore, although Mozart's body was confined to a "common grave", this does not mean that it was "communal". The word "common" was simply meant to distinguish it from the superior burial rights which pertained to the aristocracy - i.e not common!
If you are interested in reading more, check out Michael Lorenz's interested in detailed work in this area.