  We study the weak equivalence principle in the context of modified dispersion
relations, a prevalent approach to quantum gravity phenomenology. We find that
generic modified dispersion relations violate the weak equivalence principle.
The acceleration in general depends on the mass of the test body, unless the
Hamiltonian is either two-homogeneous in the test particles' 4-momenta or the
corresponding Lagrangian differs from the homogeneous case by a total
derivative only. The key ingredient of this calculation is a $3+1$
decomposition of the parametrization invariant relativistic test particle
action derived from the dispersion relation. Additionally, we apply a
perturbative expansion in the test particle's spatial velocity and the inverse
speed of light. To quantify our result, we provide a general formula for the
E\"otv\'os factor of modified dispersion relations. As a specific example, we
study the $\kappa$-Poincar\'e dispersion relation. Comparing the ensuing
non-vanishing E\"otv\'os factor to recent data from the MICROSCOPE experiment,
we obtain a bound of $\kappa^{-1}\geq10^{15}{\rm GeV}/c^2.$.
