Prosecutor Peter Fritzen said the driver, a 51-year-old Trier native, appeared to be suffering from "psychiatric problems" and had been under the influence of alcohol whilst at the wheel of his silver SUV.
Police, who have been questioning the suspect, said they had "no indications of a political motive".
Prosecutors are considering requesting that the suspect be placed in psychiatric care, Fritzen told reporters.
At the same press conference, Trier mayor Wolfram Leibe said among the dead
were a nine-month-old baby and a 73-year-old woman.
READ ALSO: Two killed as car hits shoppers in German city of Trier
"I think this is Trier's darkest day since World War II," he said.
Also killed were a 25-year-old woman and a 45-year-old man. Fifteen people
were injured, several seriously.
Malu Dreyer, premier of the state of Rhineland-Palatinate where Trier is located, expressed shock that a baby was among those killed by the driver's "insane act" and shared her condolences with all the affected families.
The baby's mother was being treated in hospital for injuries sustained in the rampage.
Witnesses had earlier described seeing people, including a young child in a stroller, being flung into the air as the car struck them.
'Traumatised'
The incident started around 1:50 pm and ended within four minutes of the first emergency calls arriving, with police intercepting the driver after he turned right off a main shopping street.
Police said he had ploughed through the streets for about a kilometre, leaving behind a trail of destruction.
Officers sealed off the area and cleared people from the city centre.
Smartphone footage from an eyewitness showed the arrest of the driver, who was seen lying face down on the street pinned down by several officers next to the damaged SUV.
He was the sole occupant of the vehicle.
An unnamed man who said he was a former neighbour of the suspect told NTV that the driver had a history of mental issues, as well as money worries and problems "with his father".
Christmas shopping
Chancellor Angela Merkel voiced her "great sadness" at the events in Trier and said her thoughts were with the relatives of those who were "so suddenly and violently ripped from their lives" and with the injured, in a message shared by her spokesman.
Early footage from the scene showed stunned shoppers huddling outside stores festooned with Christmas decorations as sirens blared in the distance.
Debris from stalls and outdoor displays was strewn along the cobbled street.
Picturesque Trier, near the border with Luxembourg, traces its history back to the Roman Empire and is often called Germany's oldest city.
Although Germany is grappling with a second coronavirus wave that has forced restaurants, bars, sports and cultural centres to close, retailers have been allowed to stay open and many people were out Christmas shopping.
"It's lucky that the Christmas market has been cancelled because of corona, or it could have been much worse," witness Frederic Fries told Welt TV.
The incident brought back memories of a truck rampage at a Berlin Christmas market that left 12 people dead in 2016, Germany's deadliest Islamist attack to date.
In January 2019, a German man injured eight people when he drove into crowds on New Year's Eve in the western cities of Bottrop and Essen. He was later taken into psychiatric care.
In April 2018, a German man ploughed his van into people seated outside a restaurant in the city of Münster, killing five before shooting himself dead. Investigators later said he had mental health problems.
READ ALSO: Ramming attack in Münster: What we know
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