The actress passed away peacefully on Friday.
It has been announced that West End theatres will dim their lights for two minutes at 7pm on Tuesday 1st October.
During her career, Dame Maggie Smith was nominated for six Olivier Awards and was the recipient of the 2010 Special Award.
Among her many stage roles, she appeared in productions of The Private Ear, The Public Eye, Hedda Gabler and Antony & Cleopatra. She also received Tony Award nominations for Private Lives (1975) and Night and Day (1979), before winning the 1990 Tony Award for Best Actress in a Play for Lettice and Lovage.
Hannah Essex, Co-CEO of the Society of London Theatre and UK Theatre, said: “Today the theatre world, and the nation, have lost an icon. Throughout her seventy-one years on stage and screen, Dame Maggie Smith was a magnificent talent and will be remembered as one of the most significant performers British theatre has ever seen. Our deepest condolences are with her family and loved ones, and we are proud to be able to honour her remarkable career in some small way.”