Indian:
God of Small Things - Arundhati Roy
A Fine Balance - Rohinton Mistry
White Tiger - Aravind Adiga
Maximum City: Bombay Lost and Found by Suketu Mehta (nonfiction)
Behind the Beautiful Forevers by Katherine Boo (nonfiction)
There's loads of Indian lit out there basically.
Chinese:
A Thousand Years of Good Prayers
and
The Vagrants, both by Yi Yun Li
Korea:
The Vegetarian by Han Kang
Mexico:
Like Water For Chocolate by Laura Esquivel
Signs Preceding The End of the World by Yuri Herrera
Congo? (Possibly a different Central African nation):
The Poisonwood Bible - Barbara Kingsolver
Nigeria:
All of Chinimanda Ngozi Adichie's books.
The Other Hand by Chris Cleave (part U.K setting)
Uzbekistan:
The Dead Lake
and
The Railway by Hamid Ismailov
Brazil:
City of God by Paolo Lina
Malaysia:
The Garden of Evening Mists by Tan Twan Eng
Portugal:
Blindness by Jose Saramago
Finland:
Anything by Tove Jansson
Afghanistan and Pakistan (also U.K.):
Anything by Nadeem Aslam
Guantanamo Boy by Anna Perera
The Reluctant Fundamentalist by Mohsin Hamid
Italy:
The Leopard by Tomasi Giuseppe de Lampedusa
Turkey:
Anything by Orhan Pamuk
Anything by Elif Shafak
Egypt:
The Map of Love by Ahmad Souief
Albania:
Chronicle in Stone by Ismail Kadare
Also:
Books by Elizabeth Laird. She writes for children by doesn't patronise and explores different cultures.
Chronicles of Ancient Darkness by Michelle Paver
Dark Matter by Michelle Paver