According to Baton Rouge newspaper The Advocate, Dr McKinney is a physician at Our Lady of the Lake Children's Hospital. The alleged assault occurred near the Louisiana State University Lakes in Baton Rouge.
Local broadcaster KATC reported that the assailant fled the scene.
The police later released an image of the attacker wearing a University of Alabama shirt and sunglasses.
A tip received by Crime Stoppers resulted in Mr McKinney's arrest following an interview with police.
The attack appears to have been referecned when Our Lady of the Lake hospital system addressed the incident in an email sent to employees.
The message indicated that one of their doctors had been "identified as the suspect in an alleged racially motivated attack that surfaced online and in the media."
“At Our Lady of the Lake, we do not tolerate hate, discrimination, or violence by any member of our organisation toward another person,” CEO Scott Wester wrote. “To be very clear, there are no excuses and no exceptions to respect one another and our community.”
The email said the doctor involved in the incident - who the hospital did not identify in the email -had been placed on leave. The hospital later confirmed to The Advocate that the email was in reference to Dr McKinney.
The doctor was released on $10,000 bond on Wednesday night.