The announcement was made just hours before she had been due to appear in the first preview performance at the Vaudeville Theatre on Wednesday.
Outhwaite's role of dance teacher Mavis will played this week by Katie Verner.
Richard Harris' comedy is about the seven women and one man who join a weekly tap dancing class.
Co-star Amanda Holden said: "It is sad to lose Tamzin. But we can assure everyone who comes a fun and entertaining evening and we can't wait to get started.
"We look forward to Tamzin returning very soon."
Outhwaite tweeted a picture of her injured foot and a pair of crutches.
Anna-Jane Casey will take up Outhwaite's role from next week until she is declared medically fit to return.
The cast includes Casey's sister Natalie, Tracy-Ann Oberman and Nicola Stephenson.
This current production opened in Bath last year and toured the UK before reaching London's West End.
Stepping Out first premiered in the the West End in 1984.
A musical film version, released in 1991, starred Julie Walters, Liza Minnelli and Shelley Winters.
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Tamzin Outhwaite has had to temporarily pull out of West End show Stepping Out after fracturing her foot.