A special court found 53-year-old guilty of removing the names of family members from the list of 2,000 Greeks with accounts in British bank HSBC in Switzerland.
The charge was reduced from a felony to a misdemeanour, and Papaconstantinou was also cleared of breach of duty in tampering with the data.
The list had been sent to Papaconstantinou in 2010 by Christine Lagarde, International Monetary Fund chief and at the time French finance minister.
Lagarde had got it from HSBC whistleblower Hervé Falciani, a former IT worker at HSBC Private Bank in Geneva.
The ex-minister risked a life term if the special tribunal had found him guilty on two counts of felony.
The verdict had been eagerly awaited as the government of left-wing Prime Minister Alexis Tsipras, elected in January, had pledged to clamp down on corruption and make government more efficient.
Similar revelations in the so-called "Lagarde List" have in recent years revealed prominent figures in Europe hiding money in Switzerland, leading to pressure on the Alpine country to dismantle its decades-old tradition of banking secrecy.