Busch, 36, becomes the latest U.S. sports figure accused of domestic violence. He won the NASCAR championship in 2004 and has won 25 NASCAR races including one this year.
The Dover Police Department said in a statement that it "can confirm that an investigation is being conducted based on an allegation of domestic assault that is alleged to have occurred in the City of Dover involving Mr. Busch."
The statement provided no details about the accuser, the circumstances of the alleged assault or when it allegedly occurred.
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Police first learned of the allegations on Wednesday and "will not have any further comment on this matter in order to preserve the integrity of the case," the statement said.
NASCAR, which holds two major races a year in Dover, issued a statement saying it was aware of the investigation.
"We recognize the seriousness of this matter and are actively gathering information from all parties, including law enforcement authorities and (Busch's race team) Stewart-Haas Racing," NASCAR Senior Vice President Brett Jewkes said.
"It would be inappropriate for NASCAR to comment further on this matter until we have more information," Jewkes added.
Busch practiced on Friday in Phoenix for the second-to-last race in the NASCAR premier series.
His team is co-owned by Tony Stewart, who was investigated by police after his car fatally struck another driver in an open-wheel sprint car race in upstate New York in August. A grand jury declined to bring criminal charges against Stewart in that case.
Busch's younger brother Kyle also races on the NASCAR circuit.
Prior to this, the most recent NASCAR premier series driver to be accused of domestic violence was Travis Kvapil, who pleaded guilty in January in North Carolina's Iredell County and was given probation, fined and sentenced to 72 hours of community service.
Kvapil, 38, has raced in 21 races in NASCAR's top series this year.
The National Football League has been rocked by a recent series of domestic violence allegations against star players including Ray Rice, Adrian Peterson and Greg Hardy.
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