No native monkeys inhabit the Dominican Republic (or Hispaniola). The island's native land mammals are limited to:
The original answer incorrectly listed two solenodon species. Haitian solenodon (S. marcanoi) is a junior synonym—same species. The Cuban solenodon (S. cubanus) is separate, in Cuba.
Monkeys (capuchins, macaques, etc.) are introduced in some Caribbean islands (St. Kitts, Barbados, Puerto Rico) but not established in DR. Feral populations exist on Mona Island (PR) and St. Croix (USVI).
Hispaniola's mammalian poverty reflects its deep-water isolation since the Cretaceous—no land bridge, no monkey rafting.