Police have since apprehended a 32-year-old from Stoke-on-Trent, in England's West Midlands, who is alleged to have sent the threats to the players via a Cricket Australia (CA) email address.
A police spokesman said the man was arrested "in connection with an allegation of making threats to kill. It appears the Australian cricket team was the target."
The man was tracked down via the email address and arrested on Friday, but was later released on bail to appear before a local court on October 27. He has not been charged with any offence.
The police spokesman said Scotland Yard's Computer Crime Unit was handling the investigation.
A CA spokesman said: "Obviously it's highly concerning and Cricket Australia acted immediately.
"There is a set procedure for dealing with these matters and that's currently being dealt with by the relevant authorities."