Excitons in nanoscale materials can exhibit fluorescence fluctuations. Intermittency is pervasive in zero-dimensional emitters such as single molecules and quantum dots. In contrast, two-dimensional semiconductors are generally regarded as stable light sources. Noise contains, however, valuable information about a material. Here, we demonstrate fluorescence fluctuations in a monolayer semiconductor due to sensitivity to its nanoscopic environment focusing on the case of a metal film. The fluctuations are spatially correlated over tens of micrometers and follow power-law statistics, with simultaneous changes in emission intensity and lifetime. At low temperature, an additional spectral contribution from interface trap states emerges with fluctuations that are correlated with neutral excitons and anticorrelated with trions. Mastering exciton fluctuations has implications for light-emitting devices such as single-photon sources and could lead to novel excitonic sensors. The quantification of fluorescence fluctuations, including imaging, unlocks a set of promising tools to characterize and exploit two-dimensional semiconductors and their interfaces.