General relativity may induce the so-called post-Newtonian correction to the inverse square law of gravity. For details, please refer to chapter 9 of Weinberg's Gravitation and Cosmology.
However, there are many research papers about testing the inverse square law on small scale (millimeter range). For example, the following two papers.
S.-Q. Yang et al., "Test of the Gravitational Inverse Square Law at Millimeter Ranges", Phys. Rev. Lett. 108, 081101 (2012).
What are they testing? Where is the correction due to general relativity?