We introduce gamma structures on regular hypergeometric $D$-modules in dimension $1$ as special one-parametric systems of solutions on the compact subtorus. We note that a balanced gamma product is in the Paley–Wiener class and show that the monodromy with respect to the gamma structure is expressed algebraically in terms of the hypergeometric exponents. We compute the hypergeometric monodromy explicitly in terms of certain diagonal matrices, Vandermonde matrices and their inverses (or generalizations of those in the resonant case).