  The proton charge radius extracted from the recent muonic hydrogen
spectroscopy [Antognini et al. 2013; Pohl et al. 2010] differs from the CODATA
2010 recommended value [Mohr et al. 2012] by more than 4% or $4.4 \sigma$. This
discrepancy, dubbed as the "Proton Radius Puzzle", is a big challenge to the
Standard Model of particle physics, and has triggered a number of works on the
quantum electrodynamic calculations recently. The proton radius puzzle may
indicate the presence of an extra correction which enlarges the 2S-2P energy
gap in muonic hydrogen. Here we explore the possibility of large extra
dimensions which could modify the Newtonian gravity at small scales and lower
the 2S state energy while leaving the 2P state nearly unchanged. We find that
such effect could be produced by four or more large extra dimensions which are
allowed by the current constraints from low energy physics.
