The Twitter message was from a man named Harry Wilson, whose profile stated that he was an Army employee.
Commenting on rumours that Allen was adopting a child, he wrote: "All the best with your new family just seen you bought s**t I mean adopted a child from Africa."
Allen informed the Ministry of Defence about the tweet, in a message that has now been removed, writing: "Do you condone (these) racist comments? He needs disciplining."
Metro quotes an Army spokesman as stating: "Racism of any kind is completely unacceptable and the Army has a zero-tolerance approach to all forms of harassment and discrimination.
Allen has subsequently received criticism for her actions, some of which she has highlighted on her Twitter account.
"Just a few examples of the drivel I'm being subjected to for reporting that guy yesterday," she wrote today (July 11).
The tweets listed included one declaring: "Good morning @lilyrosecooper you piece of low life scum! #HarryWilsonIsNotRacist #harrywilsonisahero."
It has been suggested by users that any allegation of racism hinges on whether a comma was intended before or after the word "s**t".
When one person criticised Allen for "for misreading the comment and jumping the gun", Allen replied: "No, his fault for mis-writing more like! IF that's the case, and if it is, then I'm sure his superiors will understand."