The production, which opens in the NT Olivier on 18 November 2014 (previews from 10 November), is adapted from Pulitzer Prize-winner Katherine Boo's book about the interconnected lives of people living in a Mumbai slum.
Syal last appeared at the National in Rafta, Rafta in 2007. Her other recent stage work includes Much Ado About Nothing (RSC), The Killing of Sister George (West End) and Shirley Valentine (Menier Chocolate Factory).
The National also confirmed today that, as previously reported, David Byrne and Fatboy Slim's musical Here Lies Love will open the new Dorfman Theatre (formerly the Cottesloe) in October.
The show, a conceptual musical about infamous former Philippine first lady Imelda Marcos, premiered at the Public Theater in New York last year.
Running from 13 October to 8 January (previews from 30 September), Here Lies Love is directed by Alex Timbers, with choreography by Annie-B Parson.
Physical theatre company DV8 will return to the National with John, a new verbatim work by Lloyd Newsom that will run in Lyttelton from 4 November (previews from 30 November).
It will play in rep in the Lyttelton with 3 Winters by Tena Štivičić, directed by NT associate Howard Davies, which opens on 3 December (previews from 26 November). Set in Zagreb, Croatia, the play "creates the portrait of an eclectic family, held together by the courage to survive."
Back in the Olivier Theatre, Polly Findlay's Christmas production of Bryony Lavery's adaptation of ''Treasure Island' will open on 10 December (previews from 3 December), with a cast including Patsy Ferran as Jim.
And in the NT's Temporary Theatre (formerly the Shed), Bijan Sheibani's production of Romeio and Juliet, reimagined for younger audiences by Ben Power, will return from 29 October to 14 November following a tour of London primary schools.
NT Live screenings include John on 9 December 2014 and Treasure Island on 22 January 2015.