The Banks County sheriff's office says deputies attempted to stop an SUV driven by Scott's 20-year-old brother, Antonn, for following too closely Thursday morning on Interstate 85 northeast of Atlanta.
A sheriff's news release says the vehicle failed to yield for about two miles, with speeds reaching 98 mph, before it finally pulled over. Deputies say they found more than an ounce of marijuana and 10.9 grams of MDMA, commonly called Molly.
Police say Mike Scott is charged with felony possession of marijuana and possession of a Schedule I drug. His brother faces additional charges.
The Hawks say they are aware of the situation but will have no further comment.
Mike Scott, 27, is a backup forward with the Hawks. He averaged 7.8 points per game last season.