The book, titled "Last Week Tonight with John Oliver presents A Day in the Life of Marlon Bundo," is about Vice President Mike Pence's rabbit, Marlon Bundo, falling in love with another male rabbit with whom he wishes to spend the rest of his life.
The book was written to mock a book about Pence's rabbit and Pence's stance on same-sex marriage, and it raised money for nonprofits The Trevor Project and AIDS United.
An investigation was launched after parents complained about the book, which was not approved by the Seminole County School District.
Kraig Hudson said his grandson is in the teacher's class.
"I don't think it's fair they are not telling the other parents about what they read," he said. "Noah comes home one day and asks us if it's OK for two male bunnies to get married. I said, 'By our beliefs, no. But we do not judge nobody.'"
Parent Kellie Cowart said she would have preferred that the teacher read a district-approved book to his students.
"I wouldn't mind, but I'm a very open person talking to my kids about that stuff," she said. "At the same time, a little heads-up would be nice."
Wendy Curry, whose son is gay, said the book is not age-appropriate.
"It's not something that should be in an elementary school," she said. "That's for me to decide at home -- what I want to teach my child and what I feel they are able to handle."
The teacher is remaining on the job while the internal investigation is underway.
Officials said they cannot comment on the situation until the investigation is complete.