Transport for London (TfL) said the record was set on 9 October, but was likely to be beaten by the end of the year.
The previous record was set on 28 November last year when there were 4,734,000 passengers.
The steady increase in numbers is being put down to economic and population growth.
The last week of October this year was the busiest ever week, with 28,614,000 journeys.
Overall, the number of customer journeys on the Tube has increased by a third since 2001, with the rate of growth increasing in the last five years.
London Underground managing director Nick Brown said: "The Tube is carrying more customers than ever before as London's economy and population continue to grow.
"This is why we are continuing to invest all of our income to modernise the service, improving reliability, train capacity and frequency and upgrading major stations to reduce congestion."
Mick Cash, the general secretary of the Rail, Maritime and Transport Union (RMT) said: "The increasing demand is putting the network under massive pressure day in and day out and it needs more staff and more investment to run safely and efficiently, not less.
"The case against ticket office closures, staff cuts and any further assault on budgets by the government is reinforced by today's news on passenger numbers."
