The Dutchman alleged in his autobiography that Chelsea paid an additional bonus to their players in April 2004 after a quarter-final victory over Arsenal in the Champions League tournament.
Any payments of that kind would have been in breach of Premier League rules, and Chelsea had denied the 34-year-old player's claims.
In a statement on its official website the FA confirmed Monday that the Premier League had conducted an investigation and found no evidence of bonus payments.
The FA will now look into Hasselbaink's conduct. Hasselbaink, who joined Charlton on a free transfer from Middlesbrough earlier this month, has until August 14 to respond.
Hasselbaink spent four seasons with Chelsea, before moving to Middlesbrough at the end of the 2004 season.