At 16:16GMT the Swiss franc was at 1.18947 francs per euro. The currency also reached its lowest level against the dollar since July, at 0.8195 francs per dollar.
"Should we see a continuation of the net inflow of (Swiss francs) in cash clearing accounts of our banking customers, we might have to take corrective action, within the next few days, by means of a Temporary Excess Balance Fee," UBS said in a note to its institutional investors.
"We encourage you to keep your balances in your (Swiss franc) Cash Clearing account as low as possible," it added.
The Swiss franc, considered a safe haven currency, has been rising throughout the year as investors flee economic turmoil abroad. At its peak earlier in August, it was up around 20 percent against the euro and 25 percent against the dollar compared to 2009.
Analysts at Pictet, while crediting UBS' announcement for the currency's fall on Monday, also said the worsening economic outlook announced Friday and intervention by the Swiss National Bank played a role, if only temporarily.
"The KOF Swiss leading indicator, which aims to predict the economy's direction about six months ahead, dropped to 1.61 from a downwardly revised 1.98 in July," Pictet said.
"The SNB has (also) pulled out all the stops to flood the market with Swiss francs but if the situation on the global stage were to deteriorate further, all the central bank's efforts may prove to have been in vain," it added.