Fluorescence correlation spectroscopy (FCS) is a versatile method that would greatly benefit to remote optical-fiber fluorescence sensors. However, the current state-of-the-art struggles with high background and low detection sensitivities that prevent the extension of fiber-based FCS down to the single-molecule level. Here we report the use of an optical fiber combined with a latex microsphere to perform FCS analysis. The sensitivity of the technique is demonstrated at the single molecule level thanks to a photonic nanojet effect. This offers new opportunities for reducing the bulky microscope setup and extending FCS to remote or in vivo applications.