Granada daily newspaper Ideal reported that Barral punched former Barcelona winger Cuenca after an argument during lunch at the team's training ground on Monday.
"Granada Football Club has opened disciplinary proceedings against David Barral after his involvement in an incident with Isaac Cuenca at the training ground on Nov. 21 2016," read a club statement.
"In light of the seriousness of the events, Granada Football Club has decided to provisionally suspend David Barral."
Granada are bottom with five points from 12 games and are the only Spanish top flight team without a win this season.
Spaniard Barral, 33, joined Granada in January after a short spell at United Arab Emirates club Al Dhafra.
He is reported to be close friends with Cuenca, and has posted several images on his Twitter account alongside the winger, who joined Granada a week after Barral.
(Reporting by Richard Martin; editing by Ken Ferris)
