  The Modified Newtonian Dynamics (MOND) generically predicts a violation of
the strong version of the equivalence principle. As a result the gravitational
dynamics of a system depends on the external gravitational field in which the
system is embedded. This so-called external field effect is shown to imply the
existence of an anomalous quadrupolar correction, along the direction of the
external galactic field, in the gravitational potential felt by planets in the
Solar System. We compute this effect by a numerical integration of the MOND
equation in the presence of an external field, and deduce the secular
precession of the perihelion of planets induced by this effect. We find that
the precession effect is rather large for outer gaseous planets, and in the
case of Saturn is comparable to, and in some cases marginally excluded by
published residuals of precession permitted by the best planetary ephemerides.
