In this paper, we prove a prime number theorem in short intervals for the Rankin-Selberg $L$-function $L(s,\varphi \times \varphi )$, where $\varphi$ is a fixed dihedral Maass newform. As an application, we give a lower bound for the proportion of primes in a short interval at which the Hecke eigenvalues of the dihedral form are greater than a given constant.