NHS Greater Glasgow and Clyde Public Health Protection Unit (PHPU) has confirmed the death, which health bosses said is an isolated case in Glasgow.
It is believed that contaminated heroin or a contaminated cutting agent mixed with the heroin may be responsible for the death.
The PHPU is working with Strathclyde Police to identify a possible source for the tainted drug.
Public health consultant Dr Syed Ahmed said: "This is an isolated case in Glasgow and there have been other sporadic cases in the UK and Europe in recent months.
"We are working with other services and colleagues to be on the lookout for any other possible cases especially amongst other injecting drug users."
Health bosses are now warning injecting drug users to seek urgent medical advice if they develop an infection at the site of injection.
Superintendent Grahame Clarke, from Strathclyde Police, confirmed an investigation is now under way.
He added: "I would appeal to anyone, especially drug users, to come to us with information that may enable us to trace the source of the anthrax and I'd echo NHS Greater Glasgow and Clyde's message to injecting heroin users to seek urgent medical advice if they experience an infection."