At least ten people were injured in the incident on Monday, according to local media reports.
El Espanol newspaper said the driver was a young local man who was in the car with his parents and police were not treating the accident as terrorism-related.
While most of the injured were seen at a local hospital, two people had to be taken to a bigger facility in Malaga, the provincial capital.
They included a woman with serious injuries, the National Police said in a statement.
The car's driver, a 30-year-old Spanish man, was arrested on the spot, it added.
Online videos from the scene of the crash, one of the main thoroughfares in the coastal resort city, showed ambulances and police officers while waiters cleaned up or assisted people on the ground moments after the car rammed into the pavement.
The incident took place in the mid-afternoon as the area was brimming with customers having lunch, said Raul Morote, whose family owns several restaurants on the popular Miguel Cano Avenue.
"The car was zigzagging and sweeping away everything," Mr Morote told The Associated Press.
He said he saw emergency crews attending to about a dozen people, many of them with blood covering their legs.
In 2017, an extremist Islamist cell killed 16 people and injured 140 others in two consecutive attacks by driving vehicles into groups of bystanders in Barcelona and the nearby coastal town of Cambrils.