The victims have not been named but are believed to include Syrians and Afghans. The people hit included Syrians and Afghans, some of whom suffered serious injuries.
Authorities said the driver made anti-immigrant comments during his arrest.
The German security services are reportedly treating the 50-year-old man's intentional ramming into pedestrians in Bottrop and Essen as an act of terrorism, media reported.
A picture taken on 1 January 2019 in Bottrop, Berlin, shows policemen standing in a cordoned off area at the site where a man injured four people after driving into a group celebrating the new year, in what police described as an anti-migrant attack.
A man drove a auto into pedestrians in two neighboring German cities overnight to New Year's Day, injuring four people in what police say could be attacks motivated by the xenophobic attitude of the driver.
Police said the man then headed towards the nearby town of Essen in North Rhine-Westphalia, in the western part of Germany, where he was arrested.More news: Rep. Crenshaw: Wall Crucial Part of Border Security
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Angela Lüttmann, a spokeswoman for Münster police, could not immediately confirm whether the driver was German but said he came from Essen.
The German man is accused of accelerating his auto at groups of revellers in Bottrop and Essen, two cities in the west of Germany. Police said there are indications the suspect suffered from mental illness.
According to national broadcaster NHK, the man told police he was acting in "retribution for the death penalty" without giving more precise details.
On Dec. 19, 2016, a Tunisian man ploughed a truck into a busy Christmas market in Berlin, killing 12 people.
The attack was later claimed by ISIS.
Earlier the driver had steered his vehicle at another pedestrian, who managed to escape unharmed, according to the statement.