The answer to your question greatly depends upon whose definition of a tragic hero you adhere to.
According to Aristotle, a tragic hero must possess the following ideals/characteristics: noble statue and possess greatness, occupy a high position and embody virtue, be considered great (but not perfect), the downfall is the fault of the hero, misfortune is not completely brought about by their own actions, their fall increases self-discovery, the hero's fall does not leave the audience (or reader) depressed.
According to Shakespeare, (in addition to adherence to Aristotle's characteristics) a tragic hero must possess the following ideals/characteristics: downfall due to pride, doomed from the start, typically a leader (or king), suffering must be for a reason, tragic hero is typically male.
Therefore, based upon these characteristics defined by both Aristotle and Shakespeare, Frankenstein's monster would not be considered a tragic hero if all of the characteristics are used to define him as such.
On the other hand, the monster does possess some of the characteristics which define a tragic hero: misfortune is not brought on solely by the monster (Victor is responsible), he is doomed from the start, and is suffering for a reason.
The creature is a tragic hero because he sacrifice himself to save the woman he loved.