  Small-scale dark matter structure within the Milky Way is expected to affect
pulsar timing. The change in gravitational potential induced by a dark matter
halo passing near the line of sight to a pulsar would produce a varying delay
in the light travel time of photons from the pulsar. Individual transits
produce an effect that would either be too rare or too weak to be detected in
30-year pulsar observations. However, a population of dark matter subhalos
would be expected to produce a detectable effect on the measured properties of
pulsars if the subhalos constitute a significant fraction of the total halo
mass. The effect is to increase the dispersion of measured period derivatives
across the pulsar population. By statistical analysis of the ATNF pulsar
catalogue, we place an upper limit on this dispersion of $\log \sigma_{\dot{P}}
\leq -17.05$. We use this to place strong upper limits on the number density of
ultracompact minihalos within the Milky Way. These limits are completely
independent of the particle nature of dark matter.
