Exports for the month fell 5.1 percent to 16.29 billion francs from the level a year earlier, the FCA said in a release.
Three quarters of exporters registered declines in sales as companies dropped prices to counteract the impact of the franc, which has risen sharply against the euro since January.
The pharmaceutical and chemical industries recorded the biggest drop in exports (down almost 13 percent), followed by the plastics sector (down 11.2 percent) and the food, drinks and tobacco sector (down 8.2 percent).
The machinery and electronics industries were less impacted, with exports lower by 2.2 percent, while the watchmaking sector saw sales to foreign customers decline by 0.8 percent.
On the plus side, jewellery exports rose 33 percent, while textiles increased 2.6 percent and precision instruments 1.1 percent.
Trade with Switzerland’s major trading partners in the eurozone “sharply deteriorated,” the FCA said.
The value of imports was also hit by the strong franc, declining 8.1 percent to 13.43 billion francs.
Imports from the eurozone are cheaper for Swiss customers but the evidence suggests lower prices aren't driving higher volume.
That left Switzerland with a positive trade balance of 2.9 billion francs for the month.
For the first four months of the year, Swiss exports declined 2.3 percent on a nominal basis to 66.9 billion francs, while imports dipped 5.3 percent to 55.8 billion francs.
In January, the Swiss National Bank abandoned a policy of defending a euro floor of 1.20 francs that it had pursued for more than three years, although it maintains the franc is “significantly overvalued”.
Traders have subsequently bid up the value of the franc to near parity with the euro, making Swiss products more expensive for customers in the eurozone.
With continuing worries about Greece and its future in the eurozone, the franc, a traditional safe haven currency in times of uncertainty, remains at close to historic highs against the euro.
In early morning trading on Thursday, the euro was trading at 1.03444 francs.