"The British decision will contribute to strengthening doubts about Europe's economic perspectives. This will also have a negative impact on the Swiss economy," said Schneider-Ammann, who is also economy minister.
Schneider-Amman told reporters that "the government will follow closely the effects on the exchange rate of the Swiss franc".
A stronger franc hits Swiss exporters, which are forced to squeeze costs and cut prices to remain competitive on an international market.
The Brexit vote will meanwhile have implications for Switzerland beyond the immediate economic impact, Schneider-Ammann said, warning that Bern and London now needed to find "a new basis" for their relations.
The vote will also take a toll on Switzerland's own negotiations with the EU, he said.
Switzerland, which is not a member of the EU, saw its relations with the bloc thrown into disarray when voters in February 2014 narrowly approved a referendum to curb immigration from the bloc.
Brussels reacted angrily, saying such curbs put in doubt a whole range of bilateral agreements Switzerland had signed with the EU, its main trading partner.
According to the Swiss constitution, the referendum decision must be put in place by next February, but Bern's attempts to negotiate an acceptable solution with the EU had been put on hold in anticipation of the Brexit vote.
Experts warned on Friday that Britain's decision to leave would now completely overshadow the Swiss negotiations.
Schneider-Ammann refused to "speculate on the effects" of the Brexit vote on the Swiss negotiations.
However, he acknowledged that "it is clear that the search for a solution has become more difficult with the British decision to leave the European Union".
"It is no longer foreseeable to find a solution by the end of the summer," he admitted.
The populist rightwing Swiss People's Party, which is staunchly anti-EU and anti-immigration, meanwhile said on Friday that the Brexit vote proved the folly of trying to integrate with the bloc.
The government should "immediately stop negotiations aiming to draw Switzerland closer to the EU", it concluded.