The Swedish National Food Administration (NFA) is heading the investigation, and has issued a public warning, telling people not to take Red Bull mixed with alcohol, or after heavy exercise.
The three healthy young people who died are all thought to have drunk Red Bull shortly before their deaths.
But the energy drink's manufacturers said there was no proof the deaths were linked to Red Bull.
This is one story that's been not based on facts, and has been fuelled by speculation
A spokesperson for Red Bull manufacturers
One woman, named only as Therese, 31, collapsed on the floor of a nightclub in March this year.
Her boyfriend John Andersson told a national newspaper: "Suddenly she just fell down beside me. Her heart had stopped and she was completely lifeless.
A third person died after drinking several cans of the energy drink following a heavy workout at the gym.
Doctors at Stockholm's South Hospital will lead the investigation.
Anders Glynn, of the NFA's toxicology department told BBC News Online: "The public warning is a precaution.
"At this point, its just a suspicion and we really don't know why , as it is a suspicion the physicians have reported to the press."
A spokeswoman for the manufacturers of Red Bull told BBC News Online: "This is one story that's been not based on facts, and has been fuelled by speculation."
"They need to be seen to be precautionary, but there's no proof that Red Bull is harmful when mixed."
She said the company would be working with the NFA to prove the drink was safe.
Catherine Collins, of the British Dietetic Association, said: "There's been quite a lot of research looking at are the effects of Red Bull on the heart and circulation.
"And they have shown that if you take sufficient Red Bull, and other drinks that are performance enhancing, you can lower blood pressure and that may be the cause of the problem."
Last year, the coroner at the inquest into the death of 18-year-old Ross Cooney from Limerick, called for more research into the effect of energy drinks.
Ross died of sudden adult death syndrome after a basketball match. Hours earlier he had drunk three cans of Red Bull.
The Times newspaper reports Norway, Denmark and France have classed the drink as medicinal because of its high caffeine content.
Red Bull also contains taurine, a building block for protein and helps digest food. A small amount is thought to be beneficial, but some studies have suggested a small risk to health.
Last year, one billion cans of Red Bull were bought worldwide.
The UK's Food Standards Agency said it was not planning an investigation.