They were alerted after an anonymous tip-off at the 460-pupil school - which was ranked 'good' at its most recent Ofsted inspection.
The school had sent text messages to all parents informing them of the investigation.
One parent said: "I cannot believe that I have received a text from my children's school that drugs were being dealt in the playground. Some parents should be ashamed of themselves."
Another added: "They have been caught on CCTV and the police are dealing with it."
A spokeswoman for White Meadows Primary School, in Littlehampton, West Sussex, said: "It is a police matter."
Sussex Police added: "We received a report of an apparent exchange of an item between two adults this week. No children or staff were involved.
"We are working with the school to establish the full circumstances of this isolated event."