The Swiss news agency sda reported that dozens of connections between Switzerland and Brussels were affected by the closure of Brussels- Zaventem airport, the scene of one of the attacks.
A Zurich airport spokesperson said all five flights operated by Swiss - the only airline to fly direct between Zurich and Brussels – had been cancelled.
The first scheduled flight on Thursday morning is also cancelled.
All flights to Brussels are cancelled, other flight operations are running normal at ZRH. #Brussels— Zurich Airport (@zrh_airport) March 22, 2016
Swiss said around 1,500 passengers would be affected.
At the EuroAirport in Basel three flights operated by Swiss and by easyJet were cancelled.
Geneva airport was most affected of the three biggest Swiss hubs, with 10 flights cancelled on Wednesday, sda said.
Security checks were stepped up at Swiss airports and at the borders amid nervousness following the Brussels attacks.
There was a high presence of armed cantonal police at Zurich airport on Tuesday, the Tages-Anzeiger reported.
Several dozen police officers were checking passengers in the arrivals and departure halls of Switzerland's biggest airport.
However, the Federal Office of Civil Aviation, which has the power to order a higher level of security at Swiss airports in view of a heightened threat had not done so, the paper said.
The Swiss Border Guard had also stepped up its checks in international trains and at border points, a spokesman told the paper.
The Federal Intelligence Service said on Tuesday it had no evidence of a specific threat to Switzerland.