We report the design and experimental demonstration of an electro-optically Q-switched intracavity second-harmonic generator (ISHG) based on a single aperiodically poled lithium niobate (APLN) in a 1342 nm $\text{Nd}:{\text{YVO}}_4$ laser. This intracavity APLN, designed using the aperiodic optical superlattice technique, can perform simultaneously as a laser Q switch and a second-harmonic generator. At $\sim 200\text{\hspace{0.17em} V}$ Q-switching voltage and a 5 kHz switching rate, we measured a pulse energy of $\sim 5.7\mu \text{J}$ and a peak power of $\sim 700\text{\hspace{0.17em} W}$ at 671 nm from the constructed ISHG with a 5.2 W diode power based on 51% fundamental energy depletion.