The occurrence of planets orbiting ultracool dwarfs is poorly constrained. We present results from a guest observer program on NASA's K2 spacecraft to search for transiting planets orbiting a sample of 827 ultracool dwarfs. Having found no transiting planets in our sample, we determined an upper limit on the occurrence of planets. We simulated planets orbiting our sample for a range of orbital periods and sizes. For the simulated planets that transit their host, we injected the transit light curve into the real K2 light curves, then attempted to recover the injected planets. For a given occurrence rate, we calculated the probability of seeing no planets, and use the results to place an upper limit on planet occurrence as a function of planet radius and orbital period. We find that short-period, mini-Neptune and Jupiter-sized planets are rare around ultracool dwarfs, consistent with results for early and mid-type M dwarf stars. We constrain the occurrence rate {eta} for planets between 0.5 and 10 R{earth} with orbital periods between 1 and 26.3days.