In a further sign of Germany's anger over the affair, Gabriel said the episode was "incredible" but hoped it would not "wreck" the countries' good relationship.
On April 28th, German prosecutors said they had arrested a Swiss man, identified as Daniel M., 54, who was accused of carrying out espionage activities since 2012.
According to the German media, his alleged mission was to identify German tax investigators involved in purchasing stolen data on German residents who illegally stashed their money in Switzerland.
In an interview with Deutschlandfunk radio on Saturday, Gabriel said the episode was "incredible."
He said he had discussed the affair with Swiss Foreign Minister Didier Burkhalter, who assured him that monitoring of German tax inspectors was not ongoing, as it had stopped in 2014.
Gabriel also reacted strongly to arrest warrants issued by Switzerland for German tax inspectors.
He described this move as "scandalous," adding that Germany had not yet received the warrants and would not reply to them anyway.
Since January 2006, several Germany states have bought CDs or USB sticks containing stolen data on German tax cheats, which come from Switzerland or Liechtenstein.
As a result, many of Germany's rich, powerful and famous have had to issue public apologies and paid back-taxes and fines.
Switzerland, where secrecy has been a cornerstone of the banking industry, reacted with outrage to the theft.
Berlin on Tuesday asked the Swiss ambassador, Christine Schraner Burgener, to clarify the case.
Gabriel on Saturday said he hoped that light would be shed on the affair and that German-Swiss relations would not be hurt.
"We do not wish to wreck our relationship with Switzerland, which is excellent," he said.
According to a report in Bild daily on Tuesday, the alleged Swiss spy was a former police officer and a double agent who at one stage had spied for Germany on Switzerland.
In a joint report, the Sueddeutsche Zeitung daily and public broadcasters NDR and WDR added the spy had run a paid informant inside the finance ministry of North Rhein-Westphalia, Germany's most populous state.
The information reportedly helped Swiss authorities file charges of breaching Swiss banking laws and economic espionage against three German tax investigators.
In May 2015, the EU and Switzerland signed an agreement on exchanging bank data from 2018 that will effectively end the Swiss tradition of bank secrecy for members of the bloc.