The original short story won the Hugo Award for Best Short Story in 1960. The expanded novel was joint winner of the Nebula Award for Best Novel in 1966, tied with Babel-17 by Samuel R. Delany, and was nominated for the Hugo Award for Best Novel in 1967, losing out to The Moon Is a Harsh Mistress by Robert A. Heinlein.
In the late 1960s, the Science Fiction Writers of America (SFWA) decided to give Nebula Awards retroactively and voted for their favourite science fiction stories of the era ending December 31, 1964 (before the Nebula Award was conceived). The short story version of Flowers for Algernon was voted third out of 132 nominees and was published in The Science Fiction Hall of Fame, Volume One, 1929–1964 in 1970. Keyes was elected the SFWA Author Emeritus in 2000 for making a significant contribution to science fiction and fantasy, primarily as a result of Flowers for Algernon.
Flowers for Algernon is on the American Library Association's list of the 100 Most Frequently Challenged Books of 1990–1999 at number 43. The reasons for the challenges vary, but usually center on those parts of the novel in which Charlie struggles to understand and express his sexual desires. Many of the challenges have proved unsuccessful, but the book has occasionally been removed from school libraries, including some in Pennsylvania and Texas.
In January 1970, the school board of Cranbrook, British Columbia, as well as Calgary, Alberta, removed the Flowers for Algernon novel from the local age 14-15 curriculum and the school library, after a parent complained that it was "filthy and immoral". The president of the British Columbia Teachers' Federation criticized the action. Flowers for Algernon was part of the British Columbia Department of Education list of approved books for grade nine and was recommended by the British Columbia Secondary Association of Teachers of English. A month later, the board reconsidered and returned the book to the library; they did not, however, lift its ban from the curriculum.
Flowers for Algernon has been the inspiration for works that include solo debut album A Curious Feeling by Genesis keyboardist Tony Banks and Kyosuke Himuro's debut solo album Flowers for Algernon.