Denmark’s borders closed at noon (1100 GMT) on Saturday, meaning that tourists and other foreigners who don’t have an important reason for visiting will not be allowed in.
The Danish government announced the closure late Friday and said it is to be in place until April 13.
Borders were to remain open for deliveries of medicine and food and other important goods, and not affect truck drivers, for instance, Prime Minister Mette Frederiksen said.
Danish broadcasters DR and TV2 showed cement barriers placed at 10 of the 13 land border crossings to Germany, as part of efforts to divert road traffic to the three crossings where police would check entries round the clock.
Danes will be allowed in to the country as well as people who live or work in Denmark – or people in transit.
The Danish military has been called in to assist police.
The checks apply at road, rail and ferry links, and airports.
Several ferry operators have cancelled and reduced services to neighbouring Norway and Sweden.