The 23-year-old cast member had flown from London to the US for the season two launch party in LA.
But he was caught by sniffer dogs at LAX Airport, where border officials found traces of white powder on his personal items.
A source told The Sun the “very small amount” was subsequently confirmed to be cocaine.
Heaton was then sent back to the UK, forcing him to miss the glitzy premiere of the hugely popular supernatural show.
The source said: “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.
Heaton, who has also had roles in ITV drama DCI Banks and BBC One’s Casualty, was pictured looking dishevelled near his house in London yesterday.
A representative for the Yorkshire-born star told The Sun last night: “I have no comment to make.”
It is not known if this incident will cause him further problems entering the US, where Stranger Things is filmed.
A spokesman for US Customs and Border Protection said last night: “Privacy concerns prevent us from discussing individual cases of travellers arriving at US ports of entry.
“Foreign nationals may be inadmissible due to the commission of a crime involving drug possession.”
He added that a “violation, conspiracy to violate or simply an attempt to violate” drugs laws would “render a foreign national inadmissible to the United States”.
Heaton was spotted cosying up to Brit actress Anna Friel at the Baftas in May.
Last year’s first series of Stranger Things, which also features Hollywood star Winona Ryder, bagged a string of awards, including five Emmys.
he entire cast also won a Screen Actors Guild award for “Outstanding Performance by an Ensemble in a Drama Series”.
A spokesman for Netflix did not respond to requests for comment.