A jury at Southwark Crown Court today convicted the 53-year-old Detective Chief Inspector of misconduct in a public office.
Casburn becomes the first person to be prosecuted under the Operation Elveden probe into illegal payments made by journalists to public officials.
The News of the World was shut down in July 2011 after it emerged that journalists at the paper had hacked into the voicemails of hundreds of high-profile individuals.
Prosecution lawyer Mark Bryant-Heron said that Casburn had "sought to undermine a highly sensitive and high-profile investigation".
Southwark Crown Court heard that the charge relates to September 11, 2010, when Casburn was managing the national terrorist financial investigation unit.
Her team had been tasked with running financial investigations into phone hacking as part of the Scotland Yard investigation.
It was alleged that Casburn had attempted to undermine the hacking inquiry "at the point of its launch" by contacting the newspaper under suspicion.
She attempted to argue that she made the call to alert the public that counter-terrorism officers were being tasked with investigating phone hacking rather than "saving lives".
But the jury at Southwark Crown Court unanimously decided that the mother-of-three was actually motivated by money.
Casburn has been released on bail pending a later sentencing hearing.