The euro fell to 1.1997 francs at around 11.45am before shortly recovering to trade back above the threshold again at 1.2019 francs.
A spokesman for the Swiss National Bank declined to comment to AFP whether the bank had intervened.
Since imposing the limit last year, the central bank has consistently said it would defend the level with the "utmost determination," and pledged to buy unlimited amounts of euros to keep the 1.20 francs minimum.
Investors unsettled by the eurozone debt crisis and uncertain US economic prospects have flocked to a perceived safe haven in Switzerland, driving up the value of the franc to the detriment of Swiss exporters.
The Swiss currency gained 11 percent against the euro and 15 percent against the dollar between January and September 5, 2011, when the SNB intervened decisively on foreign exchange markets to stem its rise.