Historical Fiction, Coming-of-Age, Magic Realism
Upon its publication, The History of Love was called "Jewish Magic Realism" by The New York Times. While the book might not feature such clearly magical things as a basket of invisibility (à la controversial British-Indian author Salman Rushdie's Midnight Children) or a beautiful woman floating up to heaven (One Hundred Years of Solitude by Gabriel García Márquez), it certainly shares a similar spirit with those more fantastical works, evoking the mystical and mysterious connections that unite us all.
That's not the only genre going on here, though. Magic realism is just the tip of the lit-berg (kind of like an iceberg, but with words instead of ice). We also can shelve this one under coming-of-age, since we're dealing with those oh-so-fun teen years of our protagonist, Alma. And since we're jumping around in time in the years prior to, and just after, World War II, we can slap a historical fiction label on this book as well. Now this is a book that wears a lot of hats, er, genres. It's not surprising, though, that a book about the power of, well, books would find company among multiple literary categories.