The Sun on Sunday tabloid reported boasts by an ex-player that he arranged for a Championship player to be paid 30,000 pounds (USD 49,000, 36,000 euros) to get himself a yellow card.
Gamblers can make huge sums by betting on incidents such as yellow or red cards, penalties, late goals and corner kicks.
The NCA, which deals with serious and organised crime in Britain, said it had been passed information about the alleged match-fixing from the newspaper.
"An active NCA investigation is now underway and we are working closely with the Football Association and the Gambling Commission," it said in a statement.
"Three people are in custody and are being questioned by NCA officers. We cannot comment further at this stage."
A spokeswoman told AFP the arrests had been made on Sunday but declined to identify the suspects, nor could she elaborate on what offences they were accused of.
Four people were charged this week in a separate NCA investigation into an alleged Singapore-based betting syndicate involving lower-league English football.
Speaking about Sunday's allegations, Football League chief executive Shaun Harvey said any claims of criminal activity were treated "with the utmost seriousness".
"We would encourage anyone with any evidence to report it to the police. We will be giving our full assistance to the police during their investigation," he said.
The Football Association said in a statement that it was also "working closely" with the NCA in its latest investigation.
Yesterday's allegations followed an announcement Saturday by an English non-league club that it had sacked two of its players after they were charged over match-fixing allegations.
Michael Boateng and Hakeem Adelakun, both 22, were charged this week with conspiracy to defraud contrary to common law following an investigation by the NCA.
The pair's club, Whitehawk FC, from the southern English coastal town of Brighton, said that the two men had been "dismissed with immediate effect" after an emergency board meeting.
Boateng and Adelakun, both of whom hail from south London, are scheduled to appear at Birmingham Magistrates' Court in central England on December 11.
They were the third and fourth persons to have been charged in connection with an investigation into an alleged international betting syndicate.
Chann Sankaran, a 33-year-old Singapore national, and Krishna Sanjey Ganeshan, a 43-year-old British passport-holder, were remanded in custody until December 13.
Sankaran and Ganeshan, alleged to be members of a Singapore-based betting syndicate, have been accused of conspiring to defraud bookmakers by influencing the course of football matches and placing bets on them between November 1 and November 26 this year.
The maximum sentence for the offence is 10 years' imprisonment.