The 39-year-old Algerian man is accused of daubing swastikas and anti-Jewish statements along several metres of a wall outside the synagogue on November 7, the Saxony state office of criminal investigation said.
Eyewitness accounts and surveillance videos helped them reconstruct the crime and apprehend the Dresden resident on Saturday.
“But there were no grounds for arrest,” spokesman Christian Avenarius said.
The man is not known to have previously committed politically motivated crimes.
He is now being investigated for incitement of hatred with symbols used by unconstitutional organisations, the spokesperson said. The swastika and other Nazi symbols are illegal in Germany.
Kristallnacht, or “The Night of Broken Glass,” saw Nazi thugs attack hundreds of synagogues and Jewish businesses across Germany on November 9, 1938. Some 90 Jews were killed and 30,000 Jewish men were arrested for deportation to concentration camps.