A roughly 100-metre (330-foot) section of the Carola Bridge, which connects Dresden's historic old town to other parts of the city, plunged into the Elbe River around 03:00 am (0100 GMT), the Dresden fire brigade said.
The entire area around the bridge has been sealed off.
Residents have been urged to stay away amid concerns other parts of the bridge could come crashing down.
"There is still an acute danger to life and risk of collapse," fire brigade spokesman Michael Klahre said in a video message on social media channels.
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Nobody was on or under the bridge at the time of the collapse.
"We are extremely relieved that nobody was injured," Barbara Knifka, a spokeswoman for Dresden city authorities, told the Bild newspaper.
The cause of the collapse remains unknown.
Rescue services and other experts were at the scene to assess the damage and secure the bridge, Klahre said.
Drones were being flown over the bridge to help get a clearer picture of the damage, Klahre added.
The part of the bridge that fell down contained the section dedicated to tram lines and pedestrian traffic. The section for road vehicles was not affected.
The partial collapse also damaged two major heating pipes, cutting off district heating in the city. Residents would likely be without warm water for the day, Klahre said.
The Carola Bridge is one of Dresden's main crossings. It was completed in 1971 and is named after the wife of King Albert of Saxony.
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