The footballers are all aged between 18 and 30, the National Crime Agency said.
Six other men originally arrested in December on suspicion of involvement in spot-fixing, then later bailed, have been re-arrested, the agency added.
All 13 are currently being interviewed by police over allegations of bribery and money laundering.
Spot-fixing is where a player corruptly influences a specific element of a match, for example by intentionally getting a yellow card or conceding a corner, without trying to fix the final score.

"Match-fixing, specifically spot-fixing, has become one of the biggest threats facing the integrity of sport," Sallie Barker Sport and Recreation Alliance said.
 The NCA said: "The investigation began following receipt of material from the Sun on Sunday. It remains ongoing and we cannot provide further detail at this stage.
"The six original suspects - including former Premier League player DJ Campbell - had been bailed to return on 8 April after their arrests last year. They were re-arrested following new evidence, the NCA said.
Blackburn Rovers striker DJ Campbell, former Oldham Athletic winger Cristian Montano and four others who have not been named were arrested after allegations were made in the Sun on Sunday.
Both players named denied any wrongdoing at the time. The newspaper also published allegations that former Portsmouth player Sam Sodje had told an undercover reporter that he could arrange yellow and red cards in exchange for cash.


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