Mr Fletcher, Conservative MP for Don Valley, said he wanted to "clearly set out his position" on the issue and asked head teachers to do the same.
His letter states that "boys are boys and girls are girls", and the media glamorises a "transgender lifestyle".
One school said the letter was "neither helpful nor positively received".
It was also criticised by councillors and the former boss of an LGBTQ+ youth charity, who said the comments "deny the existence" of transgender teens and could harm their mental health.
Mayor of Doncaster Ros Jones tweeted: “I would suggest our Don Valley MP focuses on the issues most affecting our communities such as the cost of living crisis and leaves our schools to educate our young people.”
His letter asks schools to confirm their position on the matter before going on to outline his own.
He describes the "trans question" as an "issue that seems to be taking over much public discourse these days".
The MP goes on to suggest that, when "it comes to feelings of being a boy or a girl", books and media have made trans "ideology acceptable to embrace".
But, he writes, it is his view that these portrayals "affirm something that is nothing more than a phase".
Mr Fletcher acknowledges some may disagree with him, but suggests that children who would previously have been dubbed Tomboys or similar may now wrongly be led to believe they are transgender.
The Free Press BBC has approached Mr Fletcher for comment.