The 27-year-old was stopped from boarding a Virgin Atlantic flight to the US at Manchester Airport on Thursday.
The Bolton-born fighter wrote on Twitter: "Visa to America was declined after i had it approved a week ago. Was looking forward to the fight. Means I'm still in England."
Khan gave no explanation as to why he was denied a visa, but the boxer's camp are reportedly trying to resolve the issue in order to get the sportsman to the MGM Grand.