Staff at Compton Care set up the quiz as a way of keeping the charity funded after experiencing a "huge collapse" in income.
Around 200 people are taking part each week from all over the world – with £11,618 being raised so far.
Natalie Wood, corporate and trusts partnership manager at the Compton Road West-based charity, said: "We're absolutely blown away to have raised more than £11,000 and it’s all thanks to the generosity, support and dedication of our loyal supporters.
"Things are all a little difficult, very uncertain and incredibly challenging at the moment, but we're so humbled that people continue to let us into their homes every Friday night to spread a little laughter.
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"This week we topped £10,000, a figure that never even crossed our minds when we started hosting these quizzes five weeks ago.
"Here at Compton Care, we're all working harder than ever to keep our services going so that we can continue to provide extraordinary care to our patients, as well as helping out our local NHS partners and district nursing teams in the fight against Covid-19. Knowing our supporters are behind us every step of the way makes it all that little bit easier."
The funds can pay for the equivalent of 15 nights on the inpatient unit, 31 night-sitting sessions, 43 visits to the Living Well Centre, 71 lymphodema sessions – or 968 freshly cooked meals for patients staying in the inpatient unit.
The quiz takes place every Friday evening from 7.45pm, with entry costing £3 per person.
People can test their general knowledge over three rounds to claim the title of Ultimate Virtual Quiz Champion – with Stones Throw Media hosting the quiz for free.
It is live streamed on Compton Care's Facebook page and held on a third-party platform called Kahoot, with people receiving a confirmation email when they signed up.
They will then be handed joining instructions with a link to follow and a pin number to enter the event.
Ms Wood added: "The quiz is just one of many ideas we have in the pipeline with the aim of helping people through this difficult time by boosting their morale and mental well-being.
"We have also launched our virtual challenge series where people can turn their hobby into a sponsored challenge to fund extraordinary care for our patients and families with all the details on our website."
Visit comptoncare.org.uk or email email@example.com