Authorities earlier advised people to remain indoors or find a safe place inside.
While synagogues in Germany are usually protected by police, worshipers and officials around the world are increasingly forced to weigh tighter security measures.
A person lies on a road in Halle, Germany, Wednesday, Oct. 9, 2019.
"It is heartbreaking to learn of yet another attack near a synagogue, this time on Yom Kippur, the holiest day of the year for Jewish people", the organization said.
Special forces policemen guard the scene.
A witness told the outlet that the gunman was dressed in military gear and armed with multiple weapons.
"The grenade hit the door and exploded", he said. Police have not yet confirmed details of the attack.
"Together with you, I would like to express my sympathies to the German police forces, the German people and the German Jewish community", European Parliament President David Sassoli told lawmakers in Brussels Wednesday.
She said it showed the attacker shooting a woman in the street after failing to enter the synagogue, then entering a business and killing another person before fleeing.
"According to the Federal Attorney General, there is sufficient evidence for a possible right-wing extremist background", he said in Berlin.
Police in the eastern German city of Halle say people are believed to have been killed in what local media reported was a shooting.
Interior Minister Horst Seehofer last month warned of the rising danger of the militant far-right, calling it "as big a threat as radical Islamism".
Mr Seehofer said that police had uncovered 1,091 weapons, including firearms and explosives, during investigations into crimes linked to the far right past year, far more than in 2017.