Police were looking for five radicalized people suspected to be part of Mourad Fares' network, the source said.
Fares, a French national, is the man who recruited Foued Mohamed-Aggad, who was identified as the third attacker at the Bataclan theater in Paris, the source said.
According to French Interior Minister Bernard Cazeneuve, Fares is a known recruiter for jihad in Syria. French intelligence sources say he's worked for ISIS, mainly in Francophone countries, and in Switzerland, including in Geneva.
He was arrested in August 2014 in Turkey and was placed in detention in France on September 11, 2014.
U.S. intelligence services provided information to Switzerland regarding four individuals plotting attacks against Switzerland and cities in the United States, the source said.
Swiss authorities then raised the terror alert level as a precaution, according to the source. Authorities in Geneva don't know whether these individuals are currently on Swiss territory, the source said.
National authorities gave Geneva authorities a description of suspects who could be in Geneva or the Geneva region. Investigations are being carried out in close collaboration with international and French police.
The source specified three factors that triggered the alert.
One was the information provided to Swiss authorities from U.S. intelligence agencies that recently intercepted communications of a group of extremists discussing the idea of attacking Geneva.
The extremists are believed to have returned to Europe after connecting with ISIS in Syria. The extremists also discussed the idea of launching attacks in Chicago and Toronto, the source said.
Second was information that an associate of Salah Abdeslam, a person suspected of having involvement in the Paris attacks, had crossed into Switzerland. Abdeslam is still at large.
And third was the identification of the third attacker at the Bataclan theater, Mohamed-Aggad. The link between a Paris attacker and the recruiter Fares generated security concerns about a Swiss associate of Fares suspected of traveling to Syria and joining with ISIS. His current whereabouts are unknown, the source said.
"We have gone from a vague threat to a precise threat," Emmanuelle Lo Verso, head of communications at the Geneva Department of Security, told CNN. She would not comment on the nature of the threat.
A statement said that the "level of vigilance" in the city has been raised and that more police have been put on the streets.
A spokesman at the United Nations complex in Geneva, Rheal LeBlanc, confirmed to CNN that U.N. security staff at entry points were armed with heavier equipment than normal.
Security measures were increased because of advice from Swiss authorities, LeBlanc said. He said no extra security staff has been added.
The Geneva complex is the second-largest U.N. center in the world, after the headquarters in New York City.
Eight attackers were killed in the November 13 Paris attacks, and two suspects are believed to be at large. They are being sought across Europe.
Abdeslam, 26, was driving toward the Belgian border hours after the attacks when police stopped and questioned him. Authorities have not said what role he may have played in the attacks.
Mohamed Abrini, 30, now the subject of an international arrest warrant, drove a car that was found abandoned in a Paris neighborhood where one of the attacks occurred. Authorities said he had dropped off one of the bombers who attacked the Stade de France.
Last month, terrorists armed with assault rifles and explosives targeted several locations across Paris, including busy restaurants, a concert hall and the Stade de France, where a soccer game between France and Germany was being played.
They killed 130 people and wounded hundreds. ISIS has claimed responsibility.