Kaplan received his bachelor of science degree from Harvard University in 1945. After pursuing a post-graduate degree for two years, he left graduate school to work for the publishing house Simon & Schuster, where he eventually became a senior editor.
Kaplan married author Anne Bernays in 1954. The two have written a double memoir entitled Back Then: Two Lives in 1950s New York, as well as The Language of Names (1997). Kaplan and Bernays live in Cambridge and Truro, Massachusetts.