Supporters going to the quarter-final will have to catch buses or walk from nearby train stations due to engineering works that mean no trains will stop at South Bermondsey station, which is next to the Den.
No trains will run between London Bridge and Streatham, and replacement bus services on that route will not stop at South Bermondsey.
Millwall have advised fans to get off at nearby stops such as Queens Road Peckham and Peckham Rye and walk to the stadium from there.
Alternatively, supporters can catch the overground train to New Cross and New Cross Gate and take a three-mile walk to the stadium.
The Bakerloo, Circle, District, and Northern underground lines are also part- or fully suspended while no overground services will run from between Surrey Quays to Clapham Junction.
Millwall have also warned anyone driving to the game that the A2 could be closed.
They have advised all supporters to check highways.gov.uk and www.tfl.gov.uk before travelling.