Western Province confirmed on Monday that one of their players was arrested on suspicion that his blood alcohol content exceeded the legal limit.
WP did not name the player.
The player was arrested at a routine road block and there is no allegation that he drove the vehicle in any untoward manner.
"WP Rugby fully supports safe and responsible road usage," the union said in a statement.
"WP Rugby will also support the player, who has an exemplary disciplinary record to date, through its employee assistance programme.
"The matter is currently being investigated by the authorities.
"Western Province Rugby thus regards the matter as sub-judice and neither WP Rugby, nor the player, will comment further."