The app uses Bluetooth wireless technology to register other phones which come into close proximity.
It works by tracing people who may unwittingly have been in prolonged contact with someone who later tested positive for the novel coronavirus.
The pilot phase, due to run until the end of May, will be limited to "a certain population group", Health Minister Alain Berset told a press conference.
In the meantime, the government will clarify the legal framework necessary for the app and submit it to parliament at the end of May, in the hope that MPs will quickly provide the green light, said Berset.
"If parliament says no, it's over" for the app, he said.
Berset also called on hackers to come forward to test the app's defences - particularly on data protection.
If the app is authorised by parliament, it will be optional and no personal data or location information will be used, the government said. COVID-19 has killed 1,525 people in Switzerland, while 30,124 have tested positive, according to daily health ministry figures out Friday.