Kostas Vaxevanis, the editor of the magazine Hot Doc, announced on his twitter account on Sunday morning that he had been arrested after publishing the list containing 2,000 names.
He also announced that he is due to face court on Monday morning.
Lagarde sent the list to the former Greek finance minister, Giorgios Papakonstantinou, in 2010 when she was still the French finance minister.
The Greek government had tried to keep the list secret since then.
The list came from an employee of the bank HSBC in Switzerland, and revealed details of around two billion euros’ worth of deposits at the HSBC branch in Geneva.
Papakonstantinou told the Greek parliament on Wednesday that he did not know what had happened to the original list, which was reportedly contained on a USB key.
The current finance minister, Yannis Sournaras, confirmed on the same day that he had asked France to resend a copy.
The list, which went viral on the internet, named three former ministers, several politicians, and Stavros Papastavros, an advisor to the Greek Prime Minister Antonis Samaras.
It also named civil servants working at the Finance Ministry, as well as several well-known businessmen, students studying abroad, pensioners and housewives.
Although it is not illegal for Greeks to hold an account outside of the country, the issue of whether wealthy Greeks are using offshore accounts to avoid taxes has created controversy.
Greek officials have long maintained that the information was illegally obtained and cannot be used in the battle against tax evasion.
Deputy Finance Minister George Mavraganis recently called the list "industrial espionage".
But mounting anger against a new round of harsh austerity cuts imposed on Greece by its international creditors has put pressure on the government to look for the list and use it to crack down on potential tax dodgers.