The Federal Office of Public Health launched a search for the man and woman earlier this week after being alerted to the risk of infection by the United States health authorities.
In a statement on Friday it said the couple had come forward and had shown no symptoms of the fatal disease.
They had been given an injection to prevent them going on to develop rabies.
The tourists were visiting the southern US state two weeks ago when they found a bat on the ground and took it to an animal clinic, the Swiss news agency SDA reported.
A test conducted a few days later showed the animal had rabies.
It was feared the Swiss couple had contracted the virus through their contact with the bat, the health office said.
The killer virus is contained in saliva and passed on through a bite or lick to a wound.
People infected with rabies can be treated as long as no symptoms are evident – a period that can last several months.
But once symptoms occur it is too late and the disease is always fatal.
Symptoms include disorientation, paralysis and delirium.
The health office said that bats in Switzerland may also carry the virus and people finding them should avoid contact.
Although Switzerland has been considered officially rabies-free since 1998 the virus is still occasionally found in bats.
Last year a man in Neuchâtel was bitten by a rabid bat, SDA said.