On Thursday, police released security footage of the incident, which shows a man in a dark shirt walking to the New Synagogue in Gdansk and throwing a stone into a window.
In a statement, police said Wednesday's incident occurred at 6pm local time (1600 GMT) in the Baltic port city of Gdansk, and appealed to anybody who recognizes the man to contact police.
They said they had spoken to witnesses and were working to determine if the act was a "hooligan prank" or one motivated by religious hatred.
Gdansk Mayor Pawel Adamowicz said he was "appalled" especially because it took place during the prayers ending Yom Kippur, the day of atonement.
"Such things should not happen in the city of freedom and solidarity," Adamowicz said, referring to Gdansk's history as the cradle of the Solidarity movement that helped topple communism.
He called on residents to gather Thursday evening outside the synagogue in a show of protest.
Poland’s chief rabbi, Michael Schudrich, said the last such incident in Poland occurred more than 20 years ago when a firebomb was thrown into the Nozyk Synagogue in Warsaw.
“What happened should never happen and must be condemned in clear and strong terms. Yet this does not represent the true face of Gdansk, the birthplace of Solidarity and freedom,” Schudrich told The Associated Press.
He said that people were gathering for prayers when the rock was thrown and that a few people were nearby, but that nobody was hurt.
The World Jewish Congress said it was "shocked and dismayed."
It said that the throwing of the rock, which entered the women's gallery, evoked "the terrible tragedies that occurred in German-occupied Poland during the years of the Holocaust."
"In recent years, Jews in Poland have been able to worship with a sense of security, and we hope that this attack does not herald negative change in that positive environment," president Ronald Lauder said.