The pan-European STOXX 600 index started the day about 2% lower, then closed down 3.3% after the announcement about Johnson's test. The declines followed a three-day rally, and the index marked its best week since 2011.
London bluechip stocks had extended losses after the news, closing 5.3% down.
With most of Europe practically under lockdown due to the virus, a recession appears imminent. EU lawmakers on Thursday extended the deadline for agreeing on a comprehensive economic rescue package by two weeks over a dispute between the ailing south and the fiscally conservative north.
"Perhaps Boris testing positive contributed to the selloff, though it would have happened anyway," said Andrea Cicione, head of strategy at TS Lombard, in London. "The bottom line is that the recovery from this crisis will be a lot slower than consensus expects. And it will be further slowed down by the high level of unemployment and lack of capex."
Stephen Innes, chief market strategist at financial services firm AxiCorp, wrote in a note: "There was no specific new coordinated action to ramp up the fiscal response to the crisis and, in particular, no agreement around 'corona bonds'."
A swathe of bumper stimulus measures from around the globe had bought about a modicum of stability in equity markets, prompting the three-day rally.
However, with the outbreak showing no signs of slowing, risk assets are likely due for more pain. Cases in the United States are now the highest in the world.
Oil and gas stocks, while dropping 4.6% on the day, outperformed their peers over the course of the week, surging about 19% as they continued to recover from a 24-year low.
European carmakers were the worst performers on the day, shedding about 5.8%.
Volkswagen fell 7.3% after its Chief Executive Herbert Diess said it may have to cut jobs if the pandemic is not brought under control, as the carmaker is still spending about 2 billion euros ($2.2 billion) a week.
Travel and leisure stocks fell 5.8%, with cruise ship operator Carnival Corp slumping nearly 21% to the bottom of the index.
Banks <.SX7P> dropped 5.4% as the European Banking Federation said they should halt 2020 dividend payments to preserve capital and continue to lend until the impact of the coronavirus epidemic is clearer.
By Ambar Warrick