The 19-year-old was seen on a surveillance video at a slot machine at the MGM Resort and Casino. The legal gambling age in Las Vegas is 21.
Brown was accompanied by her rumoured boyfriend Nick Gordon, who is 22.
The aspiring entertainer was in town to accept the Billboard Millennium award on behalf of her late mother Whitney Houston.
TMZ reports that police have now closed an investigation into the incident.
Deputy Chief David Salas of the Nevada Gambling Control Board explained that there was "not enough evidence to support criminal charges".
Bobbi Kristina will star later this year on Houston Family Chronicles, a Lifetime reality show following her mother's extended family.