According to The Sun, the British actor was flying to Los Angeles for the season two launch party when he is said to have been caught with the substance by sniffer dogs, reports dailymail.co.uk.
US border officials denied the 23-year-old entry to the country last Saturday and deported him back to London where he had flown from just hours before, claimed the report.
It meant that he was missing from the premiere of the Netflix-produced supernatural show on Thursday evening.
It is also now feared that Heaton could be barred from entering the US in future meaning he could struggle to take part in filming for "Stranger Things".
A source claimed: "He was not arrested. He was held at the airport for a while and then put back on a plane to London that night. If you are a foreign national and it is a large amount of drugs you may be charged.
"But if it is personal use, the consequences are that you will not be allowed in to the country. US law is very strict on this."
Heaton plays Jonathan Byers in the sci-fi show.