"I wanted to let you all know I made a terrible mistake last night drinking and driving and I am thankful nothing bad happened from my stupidity and I know It could have," Earnhardt wrote in a post on his Facebook page.
"I'm sorry for letting all my fans friends and family down," said Earnhardt.
The 25-year-old is the son of Kerry Earnhardt, nephew of Dale Earnhardt Jr. and grandson of NASCAR Hall of Fame member Dale Earnhardt.
Earnhardt said that he hopes he can "make it up to each and everyone of you and in the future be a good role model."
A Charleston police officer pulled Earnhardt's vehicle over Monday night after seeing it make a wide left turn at a high rate of speed, with the tires squealing through the turn. Earnhardt was charged with first-offense driving under the influence, a misdemeanor, according to a criminal complaint filed in Kanawha County Magistrate Court.
Earnhardt's eyes were glassy and his speech was slurred, and there was an odor of alcohol inside the vehicle, Cpl. R.C. Basford wrote in the complaint.
Earnhardt's blood alcohol level was .193, more than twice West Virginia's legal limit to drive of .08. He told Basford that he had had two shots of liquor at a local bar, according to the complaint.
He spent the night in the South Central Regional Jail and was released Tuesday morning following an arraignment.
If convicted, he faces up to six months in jail and a maximum $500 fine.
Earnhardt moved to Charleston from Rockingham, N.C., recently as part of a plan to gain driving experience and eventually compete in NASCAR races. He plans to race in the 2013 ARCA Truck Series, according to his website.
Earnhardt said in his Facebook post that he plans to move forward with his racing career.