Police arrested the driver, identifying him as a 33-year-old man with German citizenship.
They said there was no further danger.
"We are mourning two deaths, currently three seriously injured people, and many others who were injured," Jung told journalists at a media briefing on Monday evening, according to Leipziger Volkszeitung.
"It's impossible to find the right words for this horrific attack," he added.
Like other European countries, Germany has had a series of car-ramming and stabbing incidents in recent years, some of which involved religious or political motivations and some carried out by people with mental health issues.
The premier of the state of Saxony, Michael Kretschmer, said that the suspect had possible mental health issues, and officials said he surrendered without resistance, Leipziger Volkszeitung reported.
Police conducted a large-scale operation in the area with multiple emergency vehicles and road closures.
A city press release called it a "mass casualty event" but officials were unable to quantify the injuries.
A damaged Volkswagen SUV with a person on top of the vehicle was seen speeding through a pedestrian zone, local broadcaster Radio Leipzig reported.
The incident happened in the Grimmaische Strasse, a street that leads into central Leipzig's shopping area.
Leipzig is located southwest of Berlin and has more than 630,000 inhabitants, making it one of the biggest cities in eastern Germany.
Last year, two people were killed in the western city of Mannheim when a 40-year-old man drove a car into a group of pedestrians, only weeks after a similar attack on a trade union demonstration in Munich, killing two and injuring more than 40, many children among them.
In December 2024, several people were killed in a car-ramming attack on a Christmas market in the eastern city of Magdeburg.
That incident came months after a stabbing attack at a festival in the western city of Solingen.
with AP
