The flood level of the Elbe river was expected to reach 8.5 metres (27 feet) on Thursday, the highest since 31 March, 1845.
Hundreds of works of art in the Zwinger Palace, which houses one of Europe's great art collections including Raphael's Sistine Madonna, had to be moved to higher floors.
Water flooded both its vaults and those of the famous Semperoper opera house nearby.
Most of Dresden's ornate buildings were devastated by Allied bombing in 1945, with restoration of many only being completed in the past decade following reunification.
In another eastern city, Dessau, museum workers raced to bring the renowned modernist Bauhaus collection to higher ground as sandbags were laid to protect the centre that houses the collection, a Unesco world cultural heritage site.
'Worst natural disaster'
Many of the Saxony state capital's ornate squares were under water and about 3,000 residents have been evacuated.
The city's Royal Palace, home of Saxony kings, was also hit by floodwater while sandbags encircled the Baroque-period Frauenkirche, restored from rubble and unveiled just a few days ago.
Workers at Dresden's Semperoper pumped river water out of the basement, where it had damaged stage equipment and costumes.
Rebuilt Dresden is now one of Germany's top cultural attractions and tourist spots with many of the landmarks near the banks of the Elbe.
The main train station has now been closed for days, with water lapping the top of the windows of abandoned trains.
Saxony prime minister, Georg Mildbradt, said the flooding was the worst natural disaster the region had suffered.