No-one was injured in the blasts late Monday in a city which has become a hotspot for far-right protests amid Germany’s huge migrant influx.
“Although no-one has claimed the attack, we assume a xenophobic motive,” said Dresden police chief Horst Kretzschmar.
“We also suspect a connection with celebrations next weekend for the Day of German Unity” on Monday, October 3.
The home-made bombs went off around 2000 GMT and damaged the door of the mosque while the imam and his family were inside, forcing the partial evacuation of the hotel at the city’s international congress centre.
Dresden in Germany’s ex-communist east is the birthplace of the PEGIDA street movement, short for Patriotic Europeans Against the Islamisation of the Occident.
Its members have angrily protested against the influx of refugees and migrants that last year brought one million asylum seekers to Europe’s biggest economy.
Dresden next Monday hosts national celebrations to mark 26 years since the reunification of East and West Germany, to be attended by Chancellor Angela Merkel and President Joachim Gauck.
In an annual report outlining progress since reunification, the government warned last week that growing xenophobia and right-wing extremism could threaten peace in eastern Germany.