Crone, 60, who resigned as News International's legal manager last year, was detained on suspicion of intercepting phone communications, the Express reported. The Metropolitan Police statement did not identify him by name.
In testimony before the Leveson Inquiry, which is investigating phone hacking and other news media misconduct, Murdoch and his son James blamed Crone for the scandal, The Independent reported.
James Murdoch testified Crone and others had failed to keep him informed about what was going on, while his father said a "clever lawyer and drinking pal of the journalists" had concealed information, allowing the Murdochs to believe a single "rogue reporter" was responsible.
Crone responded with a statement that accused the elder Murdoch of trying to protect his son.
"His assertion that I 'took charge of a coverup' in relation to phone-hacking is a shameful lie," he said.
The scandal exploded last year when The Guardian reported a detective working for the Sunday tabloid News of the World had hacked into the cellphone of missing schoolgirl Milly Dowler. Crone is the 25th person to be arrested in a group that includes Murdoch's former protege, Rebekah Brooks, and Andy Coulson, who became a spokesman for Prime Minister David Cameron.