A spokesman for the Crown Office said: “Following full and careful consideration of the facts and circumstances of the case, including the currently available admissible evidence, Crown Counsel instructed that there should be no proceedings at this time.
“The Crown reserves the right to raise proceedings should further evidence become available.”
The Heather Capital liquidator has also dropped a civil claim of damages against a law firm linked to the fund.
He had been suing Burness Paull for £7.3m at the Court of Session.
A spokesman for Burness Paull said: “We considered that the allegations behind these proceedings were entirely without merit and were prepared to defend the action robustly to its conclusion.
“The proceedings attracted much media attention about the background circumstances. We are pleased that these proceedings have now been dropped.”
The liquidator is continuing an action against another law firm, Levy McRae.