Godin took an elbow to the face from Valencia goalkeeper Neto, leaving him bleeding heavily and television replays showed one of the Uruguay international's teeth flying out of his mouth.
The incident forced the 31-year-old off the field just five minutes into the second half, not long before Angel Correa netted the decisive goal.
Atleti later confirmed Godin underwent an operation to repair damage to his upper jaw, but a timescale is yet to be placed upon his recovery period.
"Diego Godin suffered an injury to his face during the match against Valencia," a statement read.
"Our defender has suffered a dentoalveolar fracture to three of his maxilla. He will undergo maxillofacial surgery in the coming days."
Atletico coach Diego Simeone was disappointed not to see Neto punished for the collision, as he felt his side deserved a penalty.
"We're going to have to kill someone to get a penalty if the Godin inciden't isn't one," he said after the game.
Madrid also lost fellow centre-back Stefan Savic to a thigh injury before half-time during a victory that left them nine points behind leaders Barcelona and the same distance above Valencia in third.