The match was planned as the second of United's three-game tour to Germany, which began with a 2-0 defeat to Union Berlin last night.
Monday's clash with FC Energie Cottbus in Dessau is unaffected and is set go ahead as planned.
A Leeds United spokesman said: "We were notified on Thursday afternoon that the game against Dresden will not go ahead on the advice of local police. We apologise to all our supporters and we are trying to establish the full facts behind the cancellation."
It comes on the same day it was revealed players were not paid in June.