The four deaths were reported at four separate addresses in the Barnsley area of South Yorkshire.
The bodies of three people – a 33-year-old man, a 40-year-old man and a 47-year-old woman were found on Friday morning.
The fourth victim, a 31-year-old man, was found dead later that night.
South Yorkshire Police said they are not formally linking the incidents at present and a coroner’s investigation is still underway to establish the cause of each death.
Officers said they are working to establish if the deaths are linked to heroin use. They are still waiting for the results of the victims' postmortem examinations and toxicology tests.
“We are very concerned,” Ian Proffitt, the temporary Chief Inspector, said.
“For four deaths to occur in similar circumstances in a small time period and in a relatively small geographical area is unusual.
“We are currently exploring to establish if they are linked to the strength or content of heroin being used locally.”
A 37-year-old man and 42-year-old man were arrested on suspicion of being involved in the supply of controlled drugs, but both have since been released.
Inspector Proffitt warned the public to “exercise caution if they come into contact with controlled drugs, particularly heroin, or heroin derivatives”.
“If you experience any unusual symptoms after taking drugs, seek medical attention immediately,” he added.
Anyone with information about the deaths or the illegal supply of drugs is asked to contact South Yorkshire Police on 101, quoting incident number 164 of 14 April or Crimestoppers anonymously on 0800 555 111.
Anyone concerned about their heroin use should seek advice from a medical professional or get help with their addiction via the NHS.