One of Lowe's attorneys, Cory Yager, said Thursday that solicitor Raines Carter, the chief prosecutor in Atlanta Municipal Court, agreed to dismiss the charges for lack of evidence.
Yager says police video following the April 28 arrest showed Lowe "did remarkably well" in his field sobriety tests after declining a breath test.
Yager told the Associated Press the reckless driving charge, which stemmed from an allegation Lowe was racing, "was absolutely unfounded."
Lowe, 37, did not contest a traffic violation for making an improper lane change.
Lowe apologized following the arrest.
The Braves were off on Thursday and open a home series against Cincinnati on Friday.