Banking and insurance shares led declines, as a rush for safety saw a drop in bond yields.
"Treasury yields were already below fair value... They're going down because they provide some insurance from large equity market moves. But when yields fall, typically the prospects of profitability for banks also come down, said said Andrea Cicione," head of strategy at TS Lombard.
Germany's Commerzbank AG was the worst performer on the bank index, closing about 5.8% lower, while insurers were bottomed out by Legal & General Group PLC.
Bucking the trend, albeit slightly, Prudential Plc, ended marginally in the black after hedge fund Third Point LLC said it had amassed a more than $2 billion stake and called on the British insurer to split into two companies.
Among individual movers, German car parts maker Leoni slumped 6% after reporting lower-than-expected core profits, while UK engineering firm Meggitt slid 5% after warning it would be hurt by the virus and Boeing's 737 MAX problems.
Sunglasses maker EssilorLuxottica closed nearly 2% lower after EU antitrust regulators on Tuesday extended their investigation into the firm's 7.2 billion-euro ($7.8 billion) bid for Dutch opticians group GrandVision by two weeks.
Euro zone data on Tuesday was also underwhelming, with figures showing German economic activity stagnated in the fourth quarter due to shrinking exports.
Germany's GDAXI fell 1.9%, while Italian shares added to Monday's decline with a 1.4% loss amid reports that major banks were curbing trips to the country as it plays host to Europe's biggest coronavirus outbreak.
Airline stocks, which took the biggest hit on Monday, also fell further, with Lufthansa, EasyJet and Ryanair ending between 1.5% to 3.6% lower.