Share prices on the SIX Swiss Exchange dropped by more than three percent at the morning opening, while the euro fell below 1.04 francs.
Shares later rebounded, although the SMI index remained down by 1.9 percent by 9.45am, and the euro rose above 1.04 francs.
Investors were responding to concerns about the Greek financial crisis after eurozone finance ministers agreed at the weekend to halt Greece's financial bailout programme.
The Greeks are set to vote in a July 5th referendum on the last offer made by Greece's creditors before talks broke down, with the government in Athens recommending that voters reject the deal.
The development has raised the spectre of Greece's exit from the eurozone and the destabilizing effect that would have on the rest of Europe.
The European Union is Switzerland's largest trading partner.
The Swiss economy has been hampered by the strength of the franc against the euro, which has been weakened by the Greek crisis and ongoing worries about a “Grexit”.
The Swiss National Bank (SNB) continues to maintain that the franc is significantly overvalued and its has introduced negative interest rates in a bid to restrain its further appreciation.
SNB Chairman Thomas Jordan told an international finance forum in Bern on Monday that the central bank had intervened to stabilize the franc in response to the Greek crisis, Neue Zürcher Zeitung reported online.
Jordan did not give details about the extent of the bank's intervention in currency trading markets.
Finance Minister Eveline Widmer-Schlumpf told the conference that Switzerland has every interest in seeing the euro increase in value against the franc, a traditional safe-haven currency in times of crisis, 20 Minuten reported.
She said politicians have been in close contact with the SNB, which is prepared for any eventuality and will take the necessary decisions as warranted, she indicated.
Stock markets elsewhere dropped precipitously in early morning trading with share prices tumbling 4.7 percent at the opening in Paris, four percent in Frankfurt and 3.3 percent in Shanghai.
The London exchange opened two percent lower.