Luxembourg has joined its European neighbours in closing schools and limiting visits to the elderly in hospitals and nursing homes, hoping to slow the spread of the coronavirus.

"Daily life is going to change and we will have to adapt," Prime Minister Xavier Bettel said on Thursday, announcing measures of a scale "never seen before" in the Grand Duchy.

Landlocked Luxembourg is home to only 600,000 people, but more than 200,000 commuters from Belgium, France and Germany cross its borders each day to come to work.

So far, the country has recorded 26 cases of COVID-19 infection, and one 94-year-old man is in a critical state in hospital.

As in many other countries touched by the virus, Luxembourg wants to encourage people to work from home, but this is complicated in its case by the tax rules for cross-border workers.