The president's son appeared on "Fox & Friends" on Wednesday to discuss the Republican National Convention. He called attention to his appearance - "glassy" eyes and a sweaty brow - during the convention and the rumours it sparked.
"I guess there must have been something with the lighting," Mr Trump Jr said.
The president's son said the claims were "ridiculous."
"When they can't attack the delivery, when they can't attack the substance, they gotta attack something," he said.
"It was [Mr Trump Jr's] keynote address, in that he looked like he had snorted a key," Mr Colbert said. "So before I tell you what he said, can we zoom in on Junior's sweaty face and wet, bloodshot eyes? Either he's high or that's what happens when you live in the splash zone of Screamin' Guilfoyle. Just bring a poncho!"
Mr Colbert was referencing the address of another RNC speaker, Kimberly Guilfoyle.
Ms Guilfoyle - who is dating Mr Trump Jr - gave a widely mocked speech at the RNC in which she shouted and gesticulated from the podium.
Mr Trump Jr took the opportunity to use the rumours to his advantage and launch an attack on his political enemies.
"They started doing this tending thing - 'Donald Trump Jr's on cocaine' and all of that - I said, no no no. You have me confused with Hunter Biden."
Mr Trump Jr has a strange fascination with Hunter Biden. He has challenged Hunter Biden to debate him and to release his tax records in an attempt to determine which son born into wealth and privilege was most born into wealth and privilege.
President Trump's request for Ukrainian president Volodymyr Zelensky to investigate Mr Biden and Hunter Biden's connection to a Ukraine-based gas company called Burisma eventually resulted in Mr Trump's impeachment. The president threatened to withhold military aid to Ukraine if Mr Zelensky didn't help him.
AUTHOR: GRAIG GRAZIOSI