We report limits in the planetary-mass regime for companions around the nearest single white dwarf to the Sun, van Maanens star (vMa 2), from deep J-band imaging with Gemini North and Spitzer IRAC mid-IR photometry. We find no resolved common proper motion companions to vMa 2 at separations from 3 - 45, at a limiting magnitude of J~23. Assuming a total age for the system of 4.1 +/-1 Gyr, and utilising the latest evolutionary models for substellar objects, this limit is equivalent to companion masses >7 +/-1 Mjup (T~300K). Taking into account the likely orbital evolution of very low mass companions in the post-main sequence phase, these J-band observations effectively survey orbits around the white dwarf progenitor from 3 - 50AU. There is no flux excess detected in any of the complimentary Spitzer IRAC mid-IR filters. We fit a DZ white dwarf model atmosphere to the optical BVRI, 2MASS JHK and IRAC photometry. The best solution gives T=6030 +/- 240K, log g=8.10 +/-0.04 and, hence, M= 0.633 +/-0.022Msun. We then place a 3sigma upper limit of 10 +/-2 Mjup on the mass of any unresolved companion in the 4.5 micron band.