Cindy Campos, whose five-year-old son was sent home with the book, claimed Dallas Independent School District were "tone deaf" for distributing the book titled Stay Safe: Run, Hide, Fight.
The cover, which features Winnie The Pooh Characters, says "if there is danger, let Winnie the Pooh and his crew show you what to do".
One of the passages includes: "If danger is near, do not fear. Hide like Pooh does until the police appear.
"Doors should be locked and the passage blocked. Turn off the light to stay out of sight."
With Texas marking the anniversary of last year's mass shooting at a school in Uvalde, which killed 19 kids and two teachers, Ms Campos has criticised the timing of the book.
She said: "It's hard because you're reading them a bedtime story and basically now you have to explain in this cute way what the book is about, when it's not exactly cute."
California's governor, Gavin Newsom, was among those who criticised the book, writing on Twitter: "Winnie the Pooh is now teaching Texas kids about active shooters because the elected officials do not have the courage to keep our kids safe and pass common sense gun safety laws."
The School Distract hit back at the criticism and claimed staff work "hard every day to prevent school shootings."
In a statement it said: "Recently a booklet was sent home so parents could discuss with their children how to stay safe in such cases.
"Unfortunately, we did not provide parents [with] any guide or context. We apologise for the confusion and are thankful to parents who reached out to assist us in being better partners."
The school district did not disclose how many pupils received the book.
The book was published by Praetorian Consulting, a Houston-based firm that provides literature on active shooter drills.
The company says on its website that it uses age-appropriate material to teach the concepts of "run, hide, fight."
In addition, the publisher was able to use the characters of Winnie The Pooh in the book due to US copyright.
The law states the works of authors are available to use by anyone 70 years after the author's death - or 95 years after publication.
It's not the first time author AA Milne's Winnie The Pooh characters has been used.
They are also being used in a recent horror film titled Winnie The Pooh: Blood and Honey, which has also received criticism.