The Mannheim public prosecutor's office said in a statement that the 40-year-old German citizen was also being charged with five counts of attempted murder alongside grievous bodily harm and 11 counts of actual boldly harm.
"Items seized from the man, in his vehicle and in his home, such as a gun, written documents and digital data carriers, are currently being forensically examined and analysed," the statement said.
An 83-year-old woman and a 54-year-old man were killed in Monday's incident.
Prosecutors have said the suspect displays evidence of a psychological disorder.
He was transferred from hospital to police custody on Tuesday.
Media reports said he received treatment after shooting himself in the mouth with a blank round as he was arrested.
Investigators searched his flat in the nearby city of Ludwigshafen late on Monday and seized a number of items, the DPA news agency has learnt.
The car involved is registered to him.
Investigators were hoping that interrogation would provide information about the motive for the incident that occurred on Monday, which police called a targeted attack.
Handwritten notes have been discovered on the car's dashboard containing mathematical formulas for speed and braking distance.
In 2010, the Mannheim public prosecutor's office brought a case against the man for the unauthorised carrying of a blank-firing gun.
He was fined by a district court.
The attack took place at the busy Paradeplatz square in central Mannheim, a city of approximately 320,000 people that lies about 80km south of Frankfurt.
Witnesses reported seeing a car speeding down a major shopping thoroughfare before striking pedestrians.
During a church service on Tuesday, the victims were remembered.
"We are startled and at the same time petrified," said the deputy dean of the Protestant church, Anne Ressel.
"The life of the city, the joy of Carnival, has been replaced by horror within minutes."
Mannheim mayor Christian Specht thanked a taxi driver of Pakistani origin who stopped the fleeing driver.
"He behaved so courageously, drove after the perpetrator and ultimately blocked his vehicle to prevent further damage," he said.
