We develop an algebraic formalism for perturbative quantum field theory(pQFT) which is based on Joyal's combinatorial species. We show that certainbasic structures of pQFT are correctly viewed as algebraic structures internalto species, constructed with respect to the Cauchy monoidal product. Aspects ofthis formalism have appeared in the physics literature, particularly in thework of Bogoliubov-Shirkov, Steinmann, Ruelle, and Epstein-Glaser-Stora. Inthis paper, we give a fully explicit account in terms of modern theorydeveloped by Aguiar-Mahajan. We describe the central construction of causalperturbation theory as a homomorphism from the Hopf monoid of set compositions,decorated with local observables, into the Wick algebra of microcausalpolynomial observables. The operator-valued distributions called (generalized)time-ordered products and (generalized) retarded products are obtained asimages of fundamental elements of this Hopf monoid under the curriedhomomorphism. The perturbative S-matrix scheme corresponds to the so-calleduniversal series, and the property of causal factorization is naturallyexpressed in terms of the action of the Hopf monoid on itself by Hopf powers,called the Tits product. Given a system of fully renormalized time-orderedproducts, the perturbative construction of the corresponding interactingproducts is via an up biderivation of the Hopf monoid, which recoversBogoliubov's formula.