The 30-year-old was released on police bail on Wednesday night, after being questioned following his arrest during the early hours of the morning.
A club statement said: “Sunderland AFC has confirmed that Titus Bramble has been suspended from duties pending the outcome of a club investigation.
“The player will not attend team training or be available for selection for matches during this period.
“The club is unable to make any further comment on the matter at present.”
As a result of his suspension, Bramble will be unavailable for Saturday’s Barclays Premier League clash with West Brom at the Stadium of Light.
Roberto Firmino says he is unconcerned as to who Liverpool will be drawn to face in the Champions League quarter-finals.