Tadeu Filippelli, a special adviser in Temer's Cabinet, and former Federal District governors José Roberto Arruda and Agnelo Queiroz were taken into custody early in the day, a police communique said.
Temer's office said in a statement that it would fire Filippelli.
Reuters could not immediately reach Filippelli, Arruda and Queiroz or their representatives. The Federal District encompasses the capital Brasilia.
Renovation of the Brasilia stadium for the 2014 World Cup cost about 1.5 billion reais ($459.38 million), prosecutors and police said in a statement, and an auditing court has said the construction included rampant overbilling.
It was the second-most expensive soccer arena in the world after the reconstruction of Wembley Stadium in London, according to the local World Cup committee's documents on spending.
Temer has resisted growing calls for his resignation after the disclosure of a recorded conversation in which he appears to condone the payment of hush money to a jailed lawmaker in a separate corruption probe.
That investigation is related to a sprawling probe into bribery and kickbacks at state oil company Petrobras that helped topple former President Dilma Rousseff last year and has sent dozens of senior politicians and business to jail.
Suspicions that many of the 12 stadiums built or renovated for the 2014 World Cup were overpriced led to street protests before and during the tournament.
Executives of construction group Odebrecht SA [ODBES.UL] in a plea bargain deal made public last month offered evidence that builders and politicians sought to fix contracts for World Cup arenas in at least six cities.
The evidence provided by Odebrecht corroborated the testimony of three executives of rival construction conglomerate Andrade Gutierrez, prosecutors said in a statement.
Brasilia does not have any soccer team in the first division of the national league so the 72,800-seat stadium is almost never filled even when games are played there.
($1 = 3.2653 reais)
(Reporting by Lisandra Paraguassu and Ueslei Marcelino; Writing by Silvio Cascione; Editing by Christian Plumb and W Simon)
