The Merchant of Venice is a romantic comedy. It is a comedy in the broadest sense of the term: nobody dies and the play has a happy ending. Though it can be dark at times, humorous moments punctuate the play, such as when Portia and Nerissa, still in disguise as lawyer and clerk, play a joke on their husbands in prevailing upon them to give up the rings the men had promised never to relinquish.
It's a romance in the sense of its fairytale-tinged plot, in which the lovely Portia must be wooed through her successful lover choosing the correct one of three caskets, and even more so in that Bassanio is willing to risk losing everything--"give and hazard all he hath"--to gain Portia's hand. If he is interested in her dowry, he is more interested in her. He genuinely loves her, calling her "fair" and of "wondrous virtue." In this play, sacrificial love triumphs: the Prince of Morocco, who desires worldly wealth, chooses the gold casket and does not win Portia, nor does the Prince of Arragon, who believes he "deserves" Portia. It's Bassanio, who willing accedes to the lead casket's demand that he risk all, who gains his beloved.
The play is a romantic comedy too in that Portia and Nerissa, after demanding their rings, admit to the joke they played, forgive, and continue to love their husbands so that all ends happily and harmoniously. Love in this play may be bounded by the pragmatic--and that is part of the comedy--but it is love all the same.