Bulgaria's ministry of interior, Director Georgi Hadzhiev, confirmed the group are being questioned by police over their involvement in racist behaviour at the Euro 2020 qualifier in Sofia on Monday night, which England won 6-0.
The ministry added that police have identified 15 people involved in the racist chants, which included monkey noises and Nazi salutes, directed at England players.
Hadzhiev said six people have been detained, three are wanted, and two have been summoned and expected to report to the police to testify.
"Work is under way to gather evidence for the others," he added.
European football governing body UEFA charged the Bulgarian Football Union (BFU) on Tuesday with four offences: racist behaviour, the throwing of objects, disruption of the national anthem and replays on a giant screen.
The English FA also had two charges brought against it: disruption of the national anthem and an insufficient number of travelling stewards.
Fans's detention came after police raided the headquarters of the Bulgarian Football Union - with its president, Borislav Mihaylov, resigning from his post after being ordered to by the country's prime minister, Boyko Borissov.
Bulgaria has come in for heavy criticism for the conduct of home fans during the game, which was played in a partially closed stadium as punishment for racist chanting by fans during a match against Kosovo in June.
Tyrone Mings, who was making his England debut, revealed he heard racist abuse in the warm-up ahead of the game.
"I think everybody heard the chants, but we stood together and we made certain decisions," he said.
England manager Gareth Southgate said he felt his players made a "major statement" on and off the pitch by refusing to let the racists win - but said they are used to racism.
"Sadly, my players, because of their experiences in our own country, are hardened to racism," Southgate said.
"I don't know what that says about our society but that's the reality, so that actually saddens me that when I speak to them about it, they are absolutely hardened to it.
"They also know they have made a statement and they want the focus to be on the football."
Bulgarian captain Ivelin Popov was seen remonstrating with home fans during half time but head coach Krasimir Balakov claimed the conversation was more likely to be about his side's poor display and he had not heard any racism during the match.
"I was concentrated on the game," Balakov said.
"I didn't actually hear anything but I just talked to the English press downstairs and I told them that if this is proven to be true, then we have to be ashamed and we have to apologise for it.
"But, once again, first it has to be proven to be true."
Ahead of the game he claimed England had a bigger problem with racism than his country did, despite 5,000 seats being left empty during the fixture as punishment for previous racist chants.