Fifth forces are ubiquitous in modified theories of gravity. To be compatible with observations, such a force must be screened on Solar System scales but may still give a significant contribution on galactic scales. If this is the case, the fifth force can influence the calibration of the cosmic distance ladder, hence changing the inferred value of the Hubble constant H₀. In this paper, we analyze symmetron screening and show that it generally increases the Hubble tension. On the other hand, by doing a full statistical analysis, we show that cosmic distance ladder data are able to constrain the theory to a level competitive with Solar System tests—currently the most constraining tests of the theory. For the standard coupling case, the constraint on the symmetron Compton wavelength is λ_C≲2.5  Mpc. Thus, distance ladder data constitutes a novel and powerful way of testing this, and similar, types of theories.