He told the media on Tuesday he had conveyed his deepest sympathy to Belgium.
The Swiss president said Switzerland and Europe stood for freedom, security, the rule of law and democracy, values which they would continue to defend.
Schneider-Ammann said he had no information about Swiss victims or of any direct threat to Switzerland.
The federal special security group had met on Tuesday afternoon and the Federal Office of Police (Fedpol) had set up a task force, he said.
The authorities were monitoring the situation.
In a statement earlier on Tuesday the Federal Intelligence Service, FIS, stressed that Switzerland was not a primary target for Islamist attacks. But as part of the West it was a possible target.
The airline Swiss cancelled a number of flights from Zurich to Brussels on Tuesday and announced the cancellation of a flight from Brussels on Wednesday morning.
Around 800 passengers are expected to be affected. Customers are being offered the chance to rebook flights free of charge.