But the BOA's director of communications Darryl Seibel said the threat "lacks credibility", and that it will not alter the rigid security arrangements already in place to protect the Great Britain team.
Federations from Italy, Germany, Hungary and Slovenia have also indicated they have received emails or letters with similar content, which were passed to the International Olympic Committee security advisers for inspection.
Seibel said: "We have received what appears to be the same e-mail that many other federations have received and the IOC has responded to state very clearly that in their view there is nothing of substance to this.
"In addition we have had our own experts take a look at this and they have responded in exactly the same way by stating that this is nothing credible.
"Organisations like ours receive correspondence of every type and it is not uncommon to come across something like this that lacks credibility.
"It is extremely important in matters such as this that everyone maintains a level head and a sensible perspective."
The International Olympic Committee also dismissed the latest threat, which comes two days after a video emerged of two young men believed to have been involved in last month's bombings in the Russian city of Volgograd.
The IOC said in a statement: "The IOC takes security very seriously and passes on any credible information to the relevant security services.
"However, in this case it seems like the email sent to a number of NOCs [national Olympic committees] contains no threat and appears to be a random message from a member of the public."