There is!

"Journey to the West" is an extremely Chinese influential work that recounts the pilgrimage of a buddhist monk to India. The story contains monsters and supernatural challenges, similar to the Odyssey.

The well known manga/animation Dragon Ball is loosely based on this work. Goku, the main character, is 'Sun Wukong' or Monkey king (in fact, Goku is just the japanese pronunounciation of 'Wukong'). He has the monkey tail. Some of the side characters, such as the piggy and the turtle master are also loosely based on characters from 'Journey to the West'.

Lastly, Jet Li's Forbidden Kingdom is also loosely based on this work. Jet Li's character is the same irreverent, authority defiant Monkey king so beloved by the readers of 'The Journey to the West'.

If 'Journey to the West' is the East's Odyssey, 'the Romance of the Three Kingdoms' would be the East's Iliad. It is a long epic historical novel that captures the turbulent era following the fall of the Han dynasty. Much like the Iliad, the Romance of the Three Kingdoms features brave and fearless warriors that challenge each other in combat. It also has political intrigue and strategy reminescent of GRRM's Game of Thrones. This work is extremely influential and widely read in China, Korea, Japan etc.

Finally, since 'Eastern Literature' is an ambiguous word, I can mention 'Shahnameh', which is the Persian equivalent of the Iliad. I've never read it and am not familiar with it, but I know it has greatly shaped the Persian language and Persian identity after Muslim conquest.

Hope you enjoy! :)