At least three footballers are reported to be among those held across the country, but the BBC understands that none is linked to professional clubs.
The NCA said the focus of the operation was a suspected international illegal betting syndicate.
It is thought the suspects are being held by police in the Midlands.
The NCA was launched this year to fight organised and serious crime.
It said it was working closely with the Gambling Commission and the Football Association.
A spokesman said: "This is an active investigation and we are unable to provide further detail at this time."
Newspaper probe
The FA said it has been made aware of the arrests.
In a statement, it said: "We have worked closely with the authorities in relation to these allegations. The FA will make no further comment at this time due to ongoing investigations."
"The Gambling Commission said it had provided advice, intelligence and expertise in supporting the investigation and continues to liaise with the NCA and FA."
The NCA said the focus of the operation was a suspected international illegal betting syndicate.
It is thought the suspects are being held by police in the Midlands.
The NCA was launched this year to fight organised and serious crime.
It said it was working closely with the Gambling Commission and the Football Association.
A spokesman said: "This is an active investigation and we are unable to provide further detail at this time."
Newspaper probe
The FA said it has been made aware of the arrests.
In a statement, it said: "We have worked closely with the authorities in relation to these allegations. The FA will make no further comment at this time due to ongoing investigations."
"The Gambling Commission said it had provided advice, intelligence and expertise in supporting the investigation and continues to liaise with the NCA and FA."
The Crown Prosecution Service said it had liaised with the NCA during its investigation.
The arrests come after an undercover investigation by the Daily Telegraph newspaper.
It carries claims that a betting syndicate fixer from Singapore discussed the possibility of influencing the scores and outcomes of lower-league English games for £50,000 at a meeting in Manchester.
According to the paper, he claimed potential gamblers would make hundreds of thousands of pounds by using the inside information through bets placed on Asian-based websites.
The fixer reportedly offered to target two football matches, saying he would tell players how many goals he needed to be scored.
He can be heard in a video claiming that he would pay a player £5,000 to take a yellow card at the start of a match as a signal that the result was likely to be fixed.
The Football League said it had not been contacted by police about the investigation.
Football League chief executive Shaun Harvey said: "The threat of corruption is something that the Football League and the other football authorities treat with the utmost seriousness.
"The integrity of our matches and our competitions is the bedrock of the domestic game."
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