Military police have launched an investigation which is understood to be running parallel to others by prison bosses and a regional drug squad.
Regional drugs squad police chief Mario Souza confirmed: 'We are investigating from the perspective of drugs trafficking.
'We are going to look into questions like when the video was taken as well as confirming the place it was taken in and investigating the context.'
Cezar Schirmer, Public Security Minister for the state of Rio Grande do Sul which Porto Alegre is part of, branded the footage 'unacceptable, provocative and nasty.'
He added in a statement released by his department: 'Cesar Schirmer has ordered a police inquiry to get to the bottom of drugs trafficking and the use of mobile phones in prison, as a result of the publication on social media of a video where inmates are consuming cocaine, supposedly in a state jail.
'The identities of those involved in the recording and the aspects of consumption and drugs trafficking, as well as the entry of drugs and mobiles into prison and the circumstances surrounding this incident and the place and date, are not yet clear. They need to be investigated fully and immediately.'