Paulo Lacerda, who leads Abin, is among those suspended from duty.
Silva's decision comes after the weekly newspaper Veja reported over the weekend that Abin had spied on Mendes and other senior officials by bugging their telephones.
Veja published transcripts of what it said was a conversation between Mendes and Demostenes Torres, an opposition senator.
According to the newspaper, Torres was asking Mendes for help in overturning a lower-court decision to keep a witness from appearing before his senate committee investigating paedophilia.
Silva said on Monday he was "concerned and indignant" over the matter while Mendes said there was "a lack of control in the state apparatus."
Opposition leaders called for a congressional investigation after the newspaper's revalations, with some calling for Silva to be impeached over what they deem his failure to keep the intelligence agency under sufficient command.
"The government has to show that it has control," Torres said.
The scandal is the latest during Silva's six-year-old administration, which had promised to clean up government and make it more accountable.
In 2005, Jose Dirceu, the president’s chief of staff, resigned after he was accused of masterminding a scheme aimed at buying votes from politicians.
Silva remains popular with the electorate, with an approval rating of about 70 per cent.