Acting on a tip-off from the domestic intelligence service, police raided an apartment but failed to find the suspect, Jaber al-Bakr, 22, who was born in Syria. He remains on the run.
Several hundred grams of "highly volatile" explosives were found at the property, investigators said.
They were destroyed by a bomb squad.
About 100 people were evacuated from the apartment building as the explosives were moved for a controlled detonation.
Two people in contact with Mr al-Bakr were detained at Chemnitz railway station and another person was detained near the apartment in the Fritz-Heckert neighbourhood, Kathlen Zink of Saxony's criminal investigation office said.
She said they were suspected of being "linked with the suspect somehow" and had been taken in for questioning.
The "where, when, how and why" of the planned attack remained unknown according to Tom Bernhardt, a spokesman for the same office.
He said the explosives in the apartment were "relatively well hidden".
Saxony police have released pictures of Damascus-born Mr al-Bakr wearing a black, hooded sweatshirt with a colourful print.
They have not provided any information about how long he had been in Germany.
They have urged anyone with information about him to come forward.
German Chancellor Angela Merkel's popularity has waned since her decision to open the borders to refugees and migrants last year, admitting more than a million people, many of them Syrian.
In July, an axe attack on a train near Wuerzburg and a suicide bombing in Ansbach wounded 20 people and were claimed by so-called Islamic State (IS).
Police in the eastern German city of Chemnitz have detained three people as they continue a search for a suspect believed to be planning a bomb attack.