Khan, an intern at a hotel in Santiago, went to the embassy after being called in for a discussion about his US visa, which had been revoked.
Police said traces of the explosive Tetryl were found on Khan's documents, bag and mobile telephone as he went through a security check at the embassy.
Tetryl is a compound used as a booster to help detonate explosive charges.
US officials say they will conduct their own investigation of the incident, but the US state department has not disclosed why Khan's American visa had been revoked.
PJ Crowley, the state department spokesman, acknowledged at a news conference on Tuesday that there might be a legitimate reason for the trace amounts of explosives.
"It's a fair question, but this is all something that will come out while we're reviewing during the course of the investigation," Crowley said.
A local newspaper, El Mercurio, reported that Khan was in Chile to study tourism.