The first observation of the concurrent production of two Formula Presented mesons in proton-nucleus collisions is presented. The analysis is based on a proton-lead (Formula Presented) data sample recorded at a nucleon-nucleon center-of-mass energy of 8.16 TeV by the CMS experiment at the CERN LHC and corresponding to an integrated luminosity of Formula Presented. The two Formula Presented mesons are reconstructed in their Formula Presented decay channels with transverse momenta Formula Presented and rapidity Formula Presented. Events where one of the Formula Presented mesons is reconstructed in the dielectron channel are also considered in the search. The Formula Presented process is observed with a significance of 5.3 standard deviations. The measured inclusive fiducial cross section, using the four-muon channel alone, is Formula Presented. A fit of the data to the expected rapidity separation for pairs of Formula Presented mesons produced in single (SPS) and double (DPS) parton scatterings yields Formula Presented and Formula Presented, respectively. This latter result can be transformed into a lower bound on the effective DPS cross section, closely related to the squared average interparton transverse separation in the collision, of Formula Presented at 95% confidence level.