The exclusive charmonium production process in (P) over barp annihilation with an associated pi 0 meson (p) over barp -> J/psi pi(0) is studied in the framework of QCD collinear factorization. The feasibility of measuring this reaction through the J/psi -> e(+) e(-) decay channel with the AntiProton ANnihilation at DArmstadt ((P) over bar ANDA) experiment is investigated. Simulations on signal reconstruction efficiency as well as the background rejection from various sources including the (P) over barp -> pi(+)pi(-)pi(0) and (p) over barp -> J/psi pi(0)pi(0) reactions are performed with PANDAROOT, the simulation and analysis software framework of the (P) over bar ANDA experiment. It is shown that the measurement can be done at (P) over bar ANDA with significant constraining power under the assumption of an integrated luminosity attainable in four to five months of data taking at the maximum design luminosity.