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The authorities added that they are trying to identify more suspects over the abuse hurled at England players during Monday's match in Sofia.
UEFA had ordered Romania to play the match behind closed doors, after failing to control their supporters.
Fourteen of those detained were foreigners, police said, adding that the arrest could not be made "without the use of coercive means."
The Netherlands take on Germany on Friday night in a qualifier for the Euro 2020 football championships.