European shares fell more than 3% in early trade.
That put the pan-European STOXX 600 on course for its worst session in over a year.
Travel and leisure stocks plunged 6.5% after Britain announced a temporary ban on flights from South Africa and neighbouring countries.
Shares in British Airways owner IAG and easyjet lost around a tenth of their value.
Oil and gas producers and miners also saw a big drop.
European investors followed where Asian markets led.
Stocks in Asia saw their sharpest drop in three months.
Japan's Nikkei was down 3% at one stage, and U.S. crude oil futures fell due to demand fears.
Japan and Australia have also hinted at possible border closures.
The new variant was detected in South Africa, Botswana and Hong Kong.
Little is known about it, but scientists said it had an unusual combination of mutations.
That could see it avoid immune responses or make it more transmissible.
