Wright, 24, was busted shortly after 3:30 a.m. after the officer saw his white Bentley drift into another lane in the area of Alton Rd. and 8th St.
The report said Wright was going 52 mph in a 35 mph zone, and nearly struck a taxi after he changed lanes without signaling.
When the officer attempted to pull Wright over, he apparently had some trouble putting his car in park.
The report noted that when the officer approached Wright, he smelled of alcohol, had red, watery eyes, and slurred his speech.
Wright didn't have up-to-date car insurance, and his driver's license was suspended, according to the report.
The officer arrested Wright for DUI and driving with a suspended license.
Wright, a native of California, has spent the past six seasons with the Heat.