The Swiss foreign affairs office (EDA) confirmed to news agencies that a Swiss woman was among the 84 killed in the Bastille Day attack, but did not state her identity.
The EDA is in contact with the victim's relatives who will receive consular assistance, it said.
On twitter, Swiss federal police said "at least" one Swiss had been killed.
Attentat de Nice: le DFAE confirme au moins une victime suisse.- fedpol (@fedpolCH) July 15, 2016
According to a newspaper in the canton of Ticino, a 54-year-old Swiss woman died in the attack.
The Corriere Del Ticino said she was on holiday on the French Riviera with her French husband when a truck rampaged through Nice killing more than 80 people.
Speaking to the paper, the victim's brother said she was hit by the truck and killed instantly.
The Swiss authorities are currently working with the French to establish if there are any more Swiss victims among the dead.
After the Swiss president expressed his shock at the attack this morning, Swiss politicians reacted throughout the morning.
A statement issued by the French-speaking city of Geneva, which borders France, said it “shared the pain of the French people and sends its condolences to the families of the victims”.
The canton of Vaud joined Geneva in expressing its “solidarity” with the French people.
In a statement the cantonal authorities said: “The Vaud government condemns in the strongest terms these terrorist acts aimed at innocents in every region of the world.”
It said was thinking of France, a “friend” of the canton, which has a large French community and “numerous cross-border links”.
The canton's security services were following the situation along with federal authorities, it added.
Politicians also took to twitter to express their solidarity with France.
The Swiss parliament tweeted its “horror” at the attack, saying it “sends its sympathy to the affected families and to the French people”.
The French embassy in Bern and consulate in Geneva has opened a book of condolences which can be signed online.