The rules will kick in at 4am on Saturday, August 30, UK time.
The move comes as Switzerland has seen infection rates rise in recent weeks, in a steep incline from infection rates reported in. June.
The country has seen 40,645 coronavirus cases, and daily cases were once as low as eight.
However, figures from the European Union show the infection rate has risen significantly in recent weeks.
READ MORE: Holidays to Cuba given green light as country added to air bridge list
The country’s new daily caseload, according to the European Centre for Disease Prevention and Control (ECDPC), is currently at 22, an increase from eight in every 10,000 people.
Some parts of Switzerland have already gone back into lockdown.
Ticino, located in the south of the country, has been in a local lockdown since July 7, and it was recently extended to September 7.
Face masks must be worn on all public transport, and at demonstrations and protests.
Cuba, however, was added to the list of safe countries from which people do not need to quarantine on return.
Mr Shapps tweeted: “Data also showed we can now add Cuba to those countries included in travel corridors.
“As with all air bridge countries, please be aware that things can (and do sometimes) change quickly.
“The decision on whether to add or remove a country is carefully made after research from the Joint Biosecurity Centre.
“A lead indicator is 20 cases per 100k over seven dates, but they take into account a wide range of factors, including level, rate and speed of change in confirmed cases.”
Patrick Ikhena, head of travel insurance at Compare The Market, warned most insurers would no longer provide cover for the three affected countries.
He said: “Switzerland, Jamaica and Czech Republic are the latest countries to be slapped with travel restrictions, with many UK holidaymakers likely to see their travel plans disrupted.
“The restrictions apply to the whole country, even those areas with low infection rates, and as a result this unfortunately means that most travel insurance policies will no longer provide cover to Switzerland, Jamaica and Czech Republic.”