The Trierischer Volksfreund local newspaper quoted an eyewitness as saying a dark grey Range Rover was driving at high speed and people had been thrown through the air.
It said the city centre had been cordoned off and helicopters were circling overhead. The mayor of Trier had rushed to the scene, and there is to be a news conference shortly, it said.
Trier is about 200 kilometers (120 miles) west of Frankfurt, near the border with Luxembourg. The city of about 110,000 people is known for its Roman gate, the Porta Nigra, which is near the scene of the crash, and as the birthplace of Karl Marx.
At least two people were killed and several others injured on Tuesday when they were hit by a car in the Western German city of Trier, police said.
Public broadcaster SWR reported that the driver had been detained by police, adding that details of the incident were unclear.
Several others were reportedly injured in the incident. Police and rescue crews are on the scene and authorities have told people to avoid the city center.
"We have arrested one person, one vehicle has been secured. Two people have died, according to preliminary indications. Please continue to avoid the downtown area," police said on Twitter.