Two men aged 35 and a 27-year-old woman all died in hospital after taking the illegal drug in the Stockton area.
Cleveland Police said street dealers were passing the batch off as a higher grade version of the drug.
A spokesman said officers were working with drug support agencies to identify the suppliers.
The first man was admitted to the University Hospital of North Tees on 5 February and died on 11 February.
A second man was admitted to the same hospital on 13 February and a woman was admitted in the early hours of 16 February. Both died on Friday.
The force spokesman added: "Obviously we don't advocate anyone should buy any type of drugs, but we are aware there are batches of particularly harmful heroin on the streets which are being peddled by dealers as a higher standard than they are."
The deaths of three people in the space of a week are being blamed on a batch of low grade heroin which is circulating on Teesside.