The incident took place in the early hours of Sunday, on West Graham Street, just hours after Sterling featured in Rangers‘ 3-1 win over Celtic.
The 26-year-old defender, who was not injured in the crash, later appeared as a substitute in Rangers’ match against Aberdeen on Tuesday.
He now faces a court appearance in connection with the alleged road traffic offence.
Police Scotland has now confirmed the charges he faces relate to alleged drink driving.
A Police Scotland spokesman said: “Officers received a report of a one-vehicle crash on West Graham Street.
“There were no injuries reported.
“The driver, a 26-year-old man, was arrested and charged.
“He is expected to appear at court at a later date.”
The Crown Office and Procurator Fiscal Service has stated that it has not yet received a report regarding the incident.
It is understood that the Rangers defender reported the crash himself and has been cooperating fully with authorities.
The club has acknowledged the incident and confirmed that it is treating the matter with seriousness.
A Rangers spokesman said: “Dujon has been cooperating with the authorities and the legal process must now take its course.
“The club takes road safety matters seriously and is clear that standards of behaviour apply to everyone representing Rangers FC.
“We will handle the matter responsibly through our internal procedures.”