Denmark, Spain and Greece are among those trying to curb infections.
And that's making investors jittery about a recovery.
European shares fell to two-week lows on Monday (Sep 21).
With a lack of U.S. stimulus also weighing on sentiment, the MSCI world equity index, which tracks shares in 49 countries, was down over 1%.
London's FTSE 100 and Germany's DAX were down 3.3 and 3.1 percent respectively.
Oil prices also fell, with Brent crude down 2.2% in early deals.
Banking shares were among the biggest losers.
That was after a media report over the weekend accused several global banks of moving large sums of allegedly illicit funds over nearly two decades.
HSBC shares plummeted to a 25-year low in Hong Kong.
The BuzzFeed and other media articles were based on leaked suspicious activity reports.
HSBC shares in London fell as much as 5.8%.
The stock has now nearly halved since the start of the year.
Standard Chartered dropped as much as 5.2% in London to its lowest since 1998. That was against the backdrop of a broader selloff in the market.
Investors will also be looking ahead to flash PMI data on Wednesday for the first hints of how economies have fared in September.
The European Central Bank will also reportedly review how long its emergency bond-purchase scheme should go on.
The European Council meets at a summit on Thursday and Friday this week.
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