Vela called in sick and skipped training at the club's Basque training ground but was later caught at a club where American pop star Chris Brown was performing.
Real Sociedad forward in trouble after skipping training for Chris Brown's concert
The Mexico international was pictured by fellow club goers and the photos were shared on Twitter
The Mexico international was pictured by fellow club goers and the photos were shared on Twitter.
He was seen alongside former team-mate Antoine Griezmann.
As a punishment, the 27-year-old has been separated from the first-team squad by coach Eusebio Sacristan, a decision backed by Real captain Xabi Prieto.
"[The coach] has decided Vela will not train and as a group we respect the decision," Prieto said in a press conference.
"It is surprising when a team-mate does not come to training. It was not taken well in the dressing room and we have told him that.
"We spoke to [Vela] and the first thing he did was show us his regret. If he could turn back time he would not do it again."