The Game -- Investigated for Domestic Violence

The Game is now the suspect in a felony domestic violence investigation ... after allegedly beating up his fiancee, law enforcement sources tell TMZ. 
According to TMZ, Game's fiancee Tiffney Cambridge, filed a police report last weekend ... following a March 19th incident during which she claims Game attacked her. Cambridge told police the couple was having an argument and Game turned violent.

Sources close to Tiffney tell TMZ, Game hit Tiffney repeatedly in the face, injuring her eye socket and breaking her nose. Law enforcement sources say police took photos of her face.

 L.A. County Sheriff's Department has launched a criminal investigation.

Both Game and Tiffney appear on his reality show, "Marrying The Game." 

Sources connected with Game tell TMZ, he acknowledges there was an incident ... but the rapper insists he never laid a finger on her.