A quantity of blood thinning medication was found placed in certain locations on shelving inside a Co-op Midcounties store in Stourport, Wyre Forest.
They had been put in the Lombard Street store on several occasions by unknown people over the last few weeks, a spokesman from West Mercia Police said.
Officers are now warning residents that if the medication was consumed by a child it could make them seriously ill.
West Mercia Police Detective Inspector Justin Taylor said: "The pills are in blister packs and are blood thinning medication.
"If the medication were to be consumed by a child it is likely they would become very unwell.
"We have been working with the store to take the appropriate measures and our local Safer Neighbourhood Team have been visiting other stores and talking with the local community to warn them to be vigilant.
"Anyone finding medication blister packs or any pills are asked to alert a staff member or pharmacist or pass the item to a health centre or police station immediately where they can safely be destroyed.
"We would also like to hear from anyone who has any information about the medication being found."
Anyone with information can call West Mercia Police on 101, quoting incident reference number 459S of July 20.