A measurement method that can be used to extract the relative intensity noise of a nanolaser is introduced and analyzed. The method is based on optical injection of emission from a nanolaser, serving as a master oscillator, transferring its intensity fluctuations to a low-noise semiconductor laser serving as a slave oscillator. Using the stochastic rate equation formalism, we demonstrate that the total relative intensity noise of the system is a weighted superposition of the relative intensity noise of individual lasers. We further discuss the analytical relations that can be used to extract the relative intensity noise spectrum of a nanolaser. Finally, we use mutual correlation as a mathematical tool to quantify the degree of resemblance between the injected and extracted intensity fluctuations, theoretically confirming that the spectra are at least 97% correlated within the 3-dB bandwidth when an injection strength is chosen properly.