The action was called by the Rail, Maritime and Transport union (RMT) in protest at plans to close all ticket offices on the "Tube" system, which they say will jeopardise hundreds of jobs and safety standards.
The strike, called after talks between union bosses and London Underground broke down earlier in the day, will cost the British capital millions of pounds.
Boards were erected outside stations offering advice to fans trying to get home from the Emirates Stadium after Arsenal hosted Newcastle in the Premier League.
But the most severe disruption is expected during Tuesday and Wednesday's rush hours.
London mayor Boris Johnson called the action, the first since the death of firebrand RMT chief Bob Crow in March, "pointless and mad".
RMT acting general secretary Mick Cash explained: "London Underground have dug themselves into an entrenched position and have refused to move one inch from their stance of closing every ticket office.
"Despite the spin from LU nothing that they are proposing is about 'modernisation'. The current plans, closing every ticket office and axing nearly a thousand safety-critical jobs, is solely about massive austerity cuts driven centrally by David Cameron and his government and implemented by Mayor Boris Johnson."
There will be a limited service on most underground lines during the strike but no trains running on the central London sections of the busy Central and Piccadilly lines and no service at all on the Waterloo and City line.
A further three-day strike is planned from 21:00 next Monday.
London's Underground system, the oldest in the world, carries around three million passengers daily.
(Ben Stansall, AFP)