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4 year oldIts borders with France, Austria and Switzerland were shut on Monday morning, except for commercial traffic.
France is considering more stringent lockdowns, with its health chief saying the situation is "deteriorating fast".
Latest World Health Organization (WHO) figures list 164,000 confirmed cases and 6,470 deaths worldwide.
However, last week it said Europe was now the "epicentre" of the virus and urged governments to act aggressively to control the spread of the Covid-19 disease.
Leaders of the G7 nations are to hold a video conference on Monday to discuss a joint response to the coronavirus pandemic.
Central banks around the world, including the US Federal Reserve and those in the UK, Japan, Canada, and Switzerland have cut interest rates and taken other measures to try to curb the economic turmoil, but stock markets in Asia and Europe still fell.
The EU's Internal Market Commissioner Thierry Breton said a recession was now expected, with a 2-2.5% negative growth.
Airlines are also continuing to slash flights as demand slumps.
Germany had tried to resist closing its borders, to try to keep the Schengen agreement on free travel between European countries working, but traffic crossing the borders with the three neighbours and also Luxembourg will now be restricted to goods and work commuters.
The aim is to stem the spread of the virus but also to curtail cross-border panic-buying, German media reported.
Only the borders with the Netherlands and Belgium are as yet unaffected.
Schools in Germany were closed on Monday, while Berlin over the weekend shut all clubs, bars and fitness centres. Large gatherings nationwide are banned.
German tourism giant TUI said on Monday it was suspending most of its operations and asked for state aid.
Germany now has close to 5,000 confirmed cases of coronavirus, and 12 deaths.
Meanwhile, Foreign Minister Heiko Maas responded to reports that US President Donald Trump wanted to buy exclusive access to a potential vaccine developed by a German biotech firm, saying: "We cannot allow others to seek exclusive results."
Germany's neighbours such as Poland, the Czech Republic and Denmark have already closed borders or introduced severe restrictions.
But there are a vast amount of travel restrictions inside many countries.
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