According to initial investigation the building was doused in flammable liquid at several points and set alight, the spokesperson said.
A resident alerted police to the fire at the synagogue on the Judengasse, which is reportedly not under constant surveillance.
Fire fighters in the city were able to put out the blaze quickly, and the building was not heavily damaged. The walls were however blackened by soot, a fire department spokesperson said.
The police search for the perpetrators has been unsuccessful so far. Officers have engaged in a widespread investigation and have called for witnesses to step forward, police said.
There were no injuries in the arson attack.
The city of Worms has called the stone building, built in 1034, one of Germany’s oldest synagogues. After being destroyed by the Nazis in 1938 the building was restored between 1958 and 1961.