North Rhine-Westphalia state's purchase of the CD - for €3.5 million has caused friction between Schäuble and his NRW counterpart Norbert Walter-Borjans.
Walter-Borjans believes buying such CDs is legitimate, even if they have been illegally acquired. The CD is believed to contain the data of around 1,000 Germans with Swiss-based assets at the private British bank Coutts.
But there is concern that such purchases could endanger a hard-won agreement between the German and Swiss governments to uncover and tax money that Germans have hidden in Swiss bank accounts.
"Random CD-purchases can only ever be a crutch - they cannot offer a thorough approach to satisfactory tax collection," Schäuble told Bild newspaper at the weekend.
"We are working towards a sustainable, credible, and long-term solution to the problem of the inadequate taxing of German taxpayers with assets in Switzerland."
Schäuble signed a tax agreement with Switzerland in September 2011, though it is yet to be approved by the upper house of the German parliament, the Bundesrat. Several states, including NRW, have threatened to block the measure in the Bundesrat.
"The agreement signed with the Swiss authorities includes a good solution for the past, with a significant lump sum payment of arrears, and for the future, with complete equality as regards fortunes kept in Germany, as well as a thorough, systematic, controlling powers on the German side," said Schäuble. "That's why we want the agreement ratified, because it will achieve all that and restore the legal peace."
But Walter-Borjans is not so happy. "In its current form, the tax agreement offers tax evaders barn-door-sized loopholes," he told Bild. "We can't agree to it as it is."
"The cases of tax evasion of German customers through Swiss banks, which have been reported in the media recently, show how big tax fraud still is," he added. "A whole of series of banks obviously offer help with tax evasion as part of their business model."
For that reason, he argued, the state was justified in purchasing CDs to investigate tax crimes.
The finance ministry has not commented on whether Schäuble's work will be affected by the collapse of his younger brother who had a heart attack last week and was put into an artificial coma. Thomas Schäuble, who runs the Rothaus brewery, collapsed while going for a walk.
The 63-year-old served various ministerial roles in the Baden-Württemberg cabinet between 1991 and 2004.