The typical characteristics of the tragedy are:
- They depict the downfall of a noble hero/heroine.
- The hero has a tragic flaw.
- The hero must undergo some sort of transformation (usually through their death).
Kafka's protagonist in Metamorphosis, Gregor, does indeed go through a transformation (both a physical and mental one). Not only does Gregor change physically, into an insect, he changes his ways of thinking. In order to make his family happy, Gregor accepts his own death as a personal sacrifice (given his family does not wish for him to be around any longer--they do not want to "deal with him").
Gregor does experience a downfall. His transformation into an insect is, beyond any doubt, a change into a lower being than that of a human.
His tragic flaw (or hamartia) is that he, in the beginning, thought to highly of himself and did not think of others first.
Therefore, if considering the characteristics of the tragedy above, Metamorphosis could be considered a tragedy.