Esther Pascaline Bombeto was arrested soon after crossing the Serbian border at night.
According to local media, the woman and her driver refused to leave the car or open the doors, arguing they benefited from diplomatic immunity.
The police eventually had to break the windows.
Reports in local media suggest Bombeto was using diplomatic passports in order to bypass customs and smuggle some 18,500 packets of cigarettes into Romania.
Her husband, Marc Marius Itela Elombola, who is the second counsellor of the Democratic Republic of Congo's embassy in Belgrade, has also been arrested on smuggling charges.
Prosecutor Mircea Andres, who is in charge of the investigation, told journalists that according to the Vienna Convention diplomats committing a felony in a country other than that to which they are accredited are not covered by immunity.