Dr Jim McMenamin, consultant in public health at Greater Glasgow Health Board, said: "We are continuing to work closely with a number of agencies to investigate the possible causes of these conditions.
Two of the users have blood stream infections and the other addict has a severe abscess, according to Greater Glasgow and Argyll and Clyde Health Boards officials.
None of the addicts, who have not been named, have necrotising fasciitis, but medical staff say they are "deeply concerned".
An outbreak control team revealed the new cases after it met to discuss the bug which has infected two users in the area.
Dr Jim McMenamin, consultant in public health at Greater Glasgow Health Board, said: "We are continuing to work closely with a number of agencies to investigate the possible causes of these conditions.
"The common link is that all of the cases have been drug injectors.
"Our advice is that drug users should not inject and if their addiction is such that they must take heroin, it should be smoked."
Dr McMenamin added: "Among other measures, our colleagues in the drugs field are reinforcing our usual message around hygiene and the sharing of equipment."
The dead addict, who has not been named, was found to have died of necrotising fasciitis at a post mortem in the Greater Glasgow area.
The examination was ordered by the procurator fiscal after two other cases of the disease were found during the last week among drug users.
More than 30 heroin users, including 18 in and around Glasgow, were killed by clostridium bacteria last year.
The outbreak team is due to meet again next week to reassess the current situation.