Kvapil, 37, was arrested after Mooresville police were called to his family home Tuesday night regarding an assault, the Charlotte Observer reported Wednesday.
Police provided no further details.
Team officials "are currently not in a position to comment or provide any details," Donato Bonquisto, a spokesman for Kvapil's team said Wednesday.
Kvapil was released on bond Wednesday following a court appearance, USA Today reported.
Ranked 31st in Sprint Cup standings, Kvapil has made about $3.2 million this year.