The US actors, both of whom are up for Emmy awards next week, will play lovelorn landowners in the off-Broadway production of the Russian classic.
The Classic Stage Company’s staging of Ivan Turgenev’s play begins its run on 9 January in New York’s East Village.
Dinklage plays Tyrion Lannister in Game of Thrones, HBO’s hit fantasy saga.
The 45-year-old, who has a form of dwarfism, will play Rakitin in the play – a long-suffering admirer of Schilling’s Natalya, the bored wife of a wealthy landowner.
Schilling, 30, is best known for her role as Piper Chapman in Orange is the New Black, the popular Netflix comedy drama set in a women’s prison.
A Month in the Country is one of a number of star-laden productions planned by the Classic Stage Company, one of New York’s most respected theatrical outfits.