The Brussels diplomat was forced to abandon face-to-face wrangling with UK negotiator Lord Frost after being ordered into self-isolation.
EU officials were frantically working to get the negotiations back on track with time running out to secure a deal.
“With David Frost we decided to suspend the negotiations at our level for a short period.
“The teams will continue their work in full respect of guidelines.”
Lord Frost said he was in “close contact” with the Frenchman to ensure the situation doesn’t derail the negotiations.
The peer added: “The health of our teams comes first. I would like to thank the European Commission for their immediate help and support.”
Under Belgian rules, anyone who has come into contact with someone who has tested positive for COVID-19 must isolate for up to 10 days.
An EU official confirmed Mr Barnier will immediately isolate in Brussels and has promised to stay in contact with Lord Frost.
The Frenchman will tomorrow update EU27 ambassadors remotely on the state of play in the Brexit negotiators.
Commission chief Ursula von der Leyen insisted the rest of her team would respect the local guidelines.
Downing Street said both sides would continue talks online as new arrangements are drawn up.
A Government spokesman said: “The Commission has informed us that an official in their delegation has tested positive for COVID-19.
“We are discussing with them the implications for the negotiations.
“We have been, and will continue to, act in line with public health guidelines to ensure the health and welfare of our teams.”
British officials had already drawn up a series of contingency measures after having reservations about resuming the trade talks in Brussels as the second wave of coronavirus ravaged the city.
And European Council President Charles Michel has warned colleagues there won’t be enough time to fully approve the future relationship pact in an agreement is not reached by Monday.
Belgian prime minister Alexander De Croo said the negotiations are now in “stoppage time” with disagreements over fishing rights and state aid rules still blocking progress.
He said: “It is time to clarify what this Brexit will look like. We are in stoppage time in the negotiations. A final agreement will have to be reached in the coming days.”
Finnish Europe minister Tytti Tuppurainen warned the talks had entered a “critical stage”.
She said: “The time pressure is huge and we all realise that time is running out.”