Silicon photomultipliers (SiPMs) are solid-state, single-photon sensitive, pixelated sensors whose usage for scintillation detection has rapidly increased over the past decade. It is known that the avalanche process within the device, which renders a single photon detectable, can also generate secondary photons which may be detected by a separate device. This effect, known as external crosstalk, could potentially degrade the science goals of future xenon dark matter experiments. In this article, we measure the effect of external crosstalk in a dual-phase, liquid xenon time projection chamber fully instrumented with SiPMs. We then consider the implications for a future xenon dark matter experiment utilizing SiPMs and discuss possible solutions.