The incidents occurred in various locations across the district, including Miramar, Brooklyn, Johnsonville, and Upper Hutt.
Jennings said an investigation is underway and police are treating the matter as a priority “given the risk to the public”.
“Police are urging the public to exercise caution, and anyone who may have this type of substance are urged not to consume it.”
People have been advised to go to their nearest healthcare provider urgently if they are feeling unwell.