Three of the deaths were reported on Friday morning and a fourth was reported on Friday evening, all in South Yorkshire.
Two men, 33 and 40, were found dead at two different addresses in Barnsley and a 47-year-old woman was found at a house in Grimethorpe.
On Friday evening, a 31-year-old man was found dead in Barnsley.
Police said: "An early line of inquiry is to establish if the deaths are linked to heroin use, although the results of post-mortem examinations and toxicology tests are awaited.
While officers are not formally linking the deaths, they have warned users of heroin or its derivatives to be cautious.
Temporary Chief Inspector Ian Proffitt said the force was "very concerned" by the deaths.
"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.
"The public should 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."
Two men, 37 and 42, have been arrested on suspicion of being concerned in the supply of controlled drugs but they have been released pending further inquiries.
Anyone with information about the deaths or the illegal supply of drugs can contact South Yorkshire Police on 101, quoting incident number 164 of 14 April or call Crimestoppers anonymously on 0800 555 111.