Wegner said the woman had been in the city with her daughter when she was killed.
He added that he had expressed his condolences to Jan Tombiński, head of the Polish embassy in Berlin.
"I am deeply moved by what happened on Saturday, and my thoughts are with you and, above all, with the daughter and the family of the murdered woman," Wegner said, according to the German news agency dpa.
"This terrorist attack was motivated by hatred. We need more cooperation, more solidarity, less hatred and fewer wars in the world," he added.
Wegner revealed the victim's nationality during the opening of an exhibition at Berlin's Red Town Hall marking the upcoming anniversary of the 1944 Warsaw Uprising, Polish state news agency PAP reported.
Polish foreign ministry spokesman Maciej Wewiór said the Polish consul in Berlin was in contact with German authorities and would provide the victim's family with consular assistance.
"We were shocked and deeply saddened to learn that the victim of the tragic attack in Berlin was a Polish citizen," Wewiór wrote on the X social media platform.
"We extend our deepest condolences to the family and loved ones of the deceased," he added.
A memorial ceremony for the woman was scheduled for Monday afternoon in front of the Brandenburg Gate in the German capital.
The attack took place late on Saturday when a man drove a van into a crowd in Berlin's Tiergarten park near the route of the Pride parade, according to media reports.
One person was killed and 29 others were injured, authorities said.
German police launched a manhunt after the attack. The suspect was shot dead on Sunday during a police operation in an allotment garden area in Berlin's Spandau district.
Authorities identified the suspect as 21-year-old Abdul B., whom security officials described as a supporter of the Islamic State group.
(gs)
Source: PAP, dpa