We apply macroscopic fluctuation theory to study the diffusion of a tracer in a one-dimensional interacting particle system with excluded mutual passage, known as single-file diffusion. In the case of Brownian point particles with hard-core repulsion, we derive the cumulant generating function of the tracer position and its large deviation function. In the general case of arbitrary interparticle interactions, we express the variance of the tracer position in terms of the collective transport properties, viz., the diffusion coefficient and the mobility. Our analysis applies both for fluctuating (annealed) and fixed (quenched) initial configurations.