Prosecutors in Frankfurt said the 29-year-old suspect was a German national who faces charges of attempted homicide over the incident in the western state of Hesse.
The investigation was continuing “in all directions”, they said in a statement, after police stopped short of calling the incident an attack.
The drama came as Germany remains on high alert following a shooting spree by a far-right gunman in the city of Hanau, also in Hesse, last Wednesday, who killed 10 people.
Eyewitness reports at the carnival parade described the driver ploughing through a barrier in a silver car and driving straight through the crowd at high speed.
“It appears to have been an intentional act,” a local police spokesman told reporters, but said the incident was not being classified as an attack until investigators had more information.
Around 30 people were injured, some of them seriously, the Frankfurt prosecutors said. Children were among those hurt.
The driver was also injured and was receiving medical care, prosecutors added.
Citing sources close to the investigation, Spiegel weekly said the driver had apparently “consumed a high level of alcohol”.
Chancellor Angela Merkel said her thoughts are with family of the victims, as she wished them “a speedy and complete recovery”, according to her spokeswoman on Twitter.
Hesse state premier Volker Bouffier said he was “shocked at the terrible act”.
But he added: “The circumstances surrounding this act remain unclear and I urge you not to speculate about possible motives.”
As in many parts of the country, residents in Volkmarsen were celebrating Rose Monday, a highlight of annual carnival festivities that sees adults and children dress up and attend parades where people play music and throw candies from floats.
In der Folge der Tat wurde vorsorglich jeder #Rosenmontagsumzug in Hessen gestoppt und abgesagt.
Derzeit liegen keine Information über eine Gefährdung andernorts vor.
Meiden Sie trotzdem größere Menschenansammlungen.
— Polizei Nordhessen (@Polizei_NH) February 24, 2020
In last week's attack in Hanau, the gunman — who left behind a racist manifesto — first opened fire at a shisha bar and a cafe, killing nine people, before shooting dead his mother and himself.
Germany's deadliest terror attack in recent history took place in 2016 when a jihadist drove his truck into a crowded Berlin Christmas market, killing 12 people.
The attacker, a failed Tunisian asylum seeker, had pledged allegiance to the Islamic State group.
The Christmas market assault prompted police across Germany to tighten security at public gatherings.
After the Hanau shootings, Interior Minister Horst Seehofer on Friday vowed to put more police at mosques, train stations, airports and borders.