Health officials said the middle-aged man's death could have been caused by injecting contaminated heroin, or a contaminated cutting agent mixed with the drug.
NHS Greater Glasgow And Clyde said it was an isolated case in the city. Police are investigating the man's death, which happened on Sunday.
Dr Syed Ahmed, public health consultant with the health board's Public Health Protection Unit, said: "We are working with other services and colleagues to be on the lookout for any other possible cases, especially amongst other injecting drug users."
Anthrax is a bacterial infection and is primarily a disease of herbivorous mammals, although other animals and some birds can also get infected.
Drug users can be exposed when heroin is contaminated with anthrax spores.
The risk to the rest of the population is negligible, officials said.
It is rare for anthrax to be spread from person to person and there is said to be no significant risk of airborne transmission from one person to another.
The Public Health Protection Unit is working with Strathclyde Police to identify a possible source of the infection.
Anthrax symptoms can include a raised, itchy, inflamed pimple, which turns into a blister with extensive swelling.
If left untreated, the infection can spread to cause blood poisoning. It can take up to a week for symptoms to develop.