London's FTSE 100 was at a two-week low, down 3.3% .FTSE and Germany's DAX fell 3.2%.
Monday's losses were in part due to rising COVID-19 cases in Europe, said Samy Chaar, chief economist at Lombard Odier.
"This is not extremely new today but you do feel that in the past days it has kind of unsettled market participants a bit because they have this new threat of localised lockdowns," he said.
European countries including Denmark, Greece and Spain have introduced new restrictions on activity.
Britain is considering a second national lockdown as new cases rise by at least 6,000 per day.
Germany's health minister said rising new infections in countries like France, Austria and the Netherlands is worrying.
Markets were also hit by a media report on how several global banks moved large sums of allegedly illicit funds over nearly two decades.
Banking shares slid after the report and HSBC shares sunk to a 25-year low in Hong Kong.
After a weak Asian session, the equity market decline accelerated when European markets opened and started to stabilise around 1030 GMT.
S&P 500 futures and Nasdaq 100 futures were both down 1.8%.
Investors will be looking ahead to flash PMI data on Wednesday for the first hints of how economies have fared in September.
"Concerns are rising that the summer recovery is probably as good as it gets when it comes to the recent rebound in economic activity," wrote Michael Hewson, chief market analyst at CMC Markets UK.
"This reality combined with the growing realisation that a vaccine remains many months away, despite President (Donald) Trump's claims to the contrary, has made investors increasingly nervous, as we head into an autumn that could see lockdowns reimposed," he said.
The dollar declined for the second week running last week, hurt by the U.S. Federal Reserve's commitment to keeping rates lower for longer.
But it rose on Monday, with the dollar index up 0.4% at 93.297 at 1132 as investors sought safer currencies.
The yen gained against the dollar for the sixth consecutive session, while the riskier Australian and New Zealand dollars, and Norwegian and Swedish crowns, lost out.
Seven members of the Fed will speak this week - including chairman Jerome Powell appearing before Congressional committees - so investors will be looking for hints to determine the dollar's direction.
The euro was down 0.4% at $1.179, while the safe Swiss franc rose against the euro EURCHF=EBS .
The benchmark 10-year German government bond yield was down 3 basis points at -0.517% DE10YT=RR , with most high-rated euro zone government bond yields down by 2-4 bps at 1137 GMT.
The European Central Bank will review how long its emergency pandemic bond purchase scheme should go on, the Financial Times reported.
The European Council meets in a summit on Thursday and Friday this week.
Elsewhere, oil prices fell, with Brent crude down 2% at $42.29 a barrel at 1138 GMT, while U.S. crude was down 2% at $40.28 a barrel.
Gold prices fell, with spot gold down 1% at $1,930.41 per ounce by 1139 GMT.
Japan has public holidays on Monday and Tuesday this week, meaning volumes are thin in Asian trading.
(Reporting by Elizabeth Howcroft; Editing by Emelia Sithole-Matarise and Andrew Cawthorne) ((Elizabeth.Howcroft@thomsonreuters.com; +44 02075427104;))