Bannatyne, 62, who has 372,000 followers on the site, used Twitter to offer a £25,000 reward "for the coward who calls himself @YuriVasilyev. Double if his arms are broken first". A few minutes later he added: "I am serious btw. I think he is in Moscow."
The post was later removed but in a statement Bannatyne said: "My family is well protected but I take any threat to them very seriously and will do all I can to ensure the person or people involved are caught."
It was unclear whether the initial offer for information leading to the arrest of the extortionist still stood, although the Dragon insisted he was closing in.
"@YuriVasilyev - My people are getting closer to you every minute, run and hide you little coward in Moscow ... Go home to your mum and cry we are closing in on you little boy."
Internet sleuths came to the Scottish tycoon's aid, offering clues and information on the identity of the person who made the threat. However, there was concern over his use of the site to offer money in return for violence.
One user asked: "You are seriously trying to pay someone, to break someone's arms, on an incredibly public forum? Fair enough. Just to clarify, you 100 per cent want everyone to know you are seriously doing this. Despite it being illegal?"
Others preferred to use the medium to poke fun at the star, who styles himself as an author, philanthropist and entrepreneur on his Twitter feed.
One suggested: "Perhaps Duncan Bannatyne should have just put up half the amount for 20 per cent of it and asked Theo to match it."
Bannatyne, who has a fortune estimated at £430 million, grew up in a council house in Clydebank earning his first money as a paper boy.
He served as a stoker on the navy ship Ark Royal but was given a dishonourable discharge after threatening to throw his commanding officer overboard. He was court-martialled and sentenced to nine months in detention.
In June he startled his Twitter followers by posting a despairing message prompting concern over the state of his four-year marriage to wife Joanne.
He wrote: "My day could not have been worse. Suicide is a considered option." Earlier he had posted: "Is death the end? Or is there more?"
The following week the problems appeared to have eased when he issued a more optimistic tweet.
- Independent