Smeets sent the video to Warsaw Home, a trade fair in Poland where he had been due to give a lecture today.
Titled "Where the hell is Job Smeets!" the video features Smeets surrounded by objects created by his Studio Job brand.
"I can't be with you today," Smeets says in the video. "You might have been told that I'm in New York now but I feel that I have to tell you the real truth."
"Last week we were at an opening in London of a really good friend of mine, the artist Maurizio Cattelan," he continues. "And at the end of the opening, a £5 million gold toilet got stolen."
Toilet disappeared from Blenheim Palace last month
The toilet, titled America, was part of an exhibition of Cattelan's work that opened at Blenheim Palace in Oxfordshire last month.
The toilet disappeared in the early hours of 14 September, the morning after the private view attended by Smeets and his partner Rebecca Sharkey. A police investigation has so far led to the arrest of two men, both British.
At the time there was suspicion that the theft was a prank orchestrated by Cattelan, a mischievous Italian artist known for playing practical jokes.
"I wish it was a prank," said Cattelan at the time. He said the incident was "deadly serious if even a little bit surreal since the subject of the robbery was a toilet".
Gufram director joins Smeets in spoof video
Police yesterday issued CCTV images of a navy blue Volkswagen Golf thought to have been used in the raid, while insurers offered a reward of £100,000 for the item's return.
Charley Vezza, director of design brand Gufram, also appears in the video issued by Smeets.
Vezza claims police are "pushing" Smeets. "He cannot leave the country," adds Vezza, who is friends with both Smeets and Cattelan and has produced products by both.
"But it cannot be him," Vezza continues. "He's a good friend of Maurizio. It's a tragic moment. I don't think Job stole it."
The functional toilet was installed in a small panelled room at Blenheim Palace, the ancestral home of Sir Winston Churchill. Guests at the private view were allowed to use the toilet for a few minutes.
Warsaw Home plays video in lieu of Smeets' lecture
Warsaw Home organisers said Smeets had told them two days ago that he could not deliver his lecture. Instead they played the video at Design Forum, the talks programme at the fair.
Smeets ends the video by saying: "And here I am under house arrest in Milan, and I'm not allowed to go anywhere."
"But I promise you, next year I'll be there," Smeets continues. "For now I'm very sorry to the organisation, to my friends in design, and also the other guests of honour."
"I was going to give you a presentation about how we all should stop designing and how all the other designers are full of crap. Next year I'll give you the best f*cking presentation you ever had."
Warsaw Home takes place at Ptak Warsaw Expo in the Polish capital until 6 October. Designer Tom Dixon and Dezeen founder and editor-in-chief Marcus Fairs were guests of honour at the show, the largest furniture and design fair in Poland, which is now in its fourth year.