The show was staged by Gurinder Chadha, who also directed the hit 2002 movie that launched the careers of Keira Knightley and Parminder Nagra.
It has had offers to tour the UK and overseas, a statement said.
"Bend It Like Beckham will continue to defy expectations and proudly represent and celebrate the UK we all know and love," Chadha said.
With a cast including Natalie Dew and Lauren Samuels, the show officially opened at the Phoenix Theatre last June following a month of previews.
It received glowing reviews - the Daily Telegraph declared it a "bold, beautifully British triumph" and the Evening Standard called it a "joyous hymn to girl power".
The final performance will take place on 5 March. A statement said: "The producers are currently finalising both national and international touring offers including a tour of India visiting multiple stadia."
While its creators may have hoped the show would stick in the West End for a more substantial run, Bend it Like Beckham has lasted for longer than some other recent British film adaptations.
Made in Dagenham lasted six months, while The Full Monty closed after just five weeks.
Chadha said the show had "inspired and entertained people of all ages and all backgrounds, something I have not seen in the West End for many years".
As well as directing, Chadha co-wrote the script with Paul Mayeda Berges. The musical includes songs composed by Howard Goodall, with lyrics by Charles Hart.
Chadha continued: "I set out to tell our stories from my perspective of our multicultural London. Our show celebrates all of us on stage and behind the scenes, something myself and the team worked so well together to realise.
"From the responses I have received since we opened there is a genuine hunger for us to tell our story internationally, so as well as planning a UK tour for the show, we are now working on expanding the production for a proposed tour of India to include multiple stadia."
The Bend It Like Beckham stage musical is to close in March, less than a year after it opened in London's West End.