In a statement published on Wednesday, the judge said the investigation suggested that of at least 2.4 million euros withdrawn from the club's accounts, 250,000 euros was paid to Espanyol players to draw 1-1 with Osasuna on the penultimate matchday.
A further 650,000 euros had been given to Real Betis players, he added, 400,000 to beat Real Valladolid on the penultimate matchday and 250,000 to lose to Osasuna on the final day of the campaign.
"The judge continues to investigate other matches, the results of which were allegedly altered by Osasuna, as well as the destination of the rest of the money taken out of the club's accounts in cash," the statement said.
Pamplona-based Osasuna, Valladolid and Seville-based Betis were all relegated to the second division, with Osasuna narrowly avoiding the drop to the third tier last season.
Betis won promotion back to the top flight and Valladolid finished fifth.
The matches are the latest to come under suspicion in recent months in a league in which it has long been suspected that games are manipulated by teams trying to avoid relegation.
In December, then-Japan coach Javier Aguirre, Manchester United midfielder Ander Herrera, Atletico Madrid captain Gabi and 38 others were named in an alleged case of match-fixing involving a game in the 2010-11 season. All deny wrongdoing.
Mexican Aguirre, who was in charge at Espanyol in 2013-14 and had an earlier stint at Osasuna, was fired by the Japan Football Association in February amid fears the scandal could affect the team's bid to qualify for the World Cup.
The judge investigating Osasuna also said he had opened a related probe into former president Pachi Izco and his board over what happened to some 3 million euros taken out in cash from the club's accounts between 2003 and 2007.
(Reporting by Iain Rogers, editing by Ed Osmond)
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