RSC managers were forced to send out the letter after the production was criticised as "sexually explicit" by teachers who walked out during a performance, taking pupils with them.
The children, from Our Lady of the Assumption Roman Catholic primary school in Coventry, walked out of the production at Stratford-upon-Avon after watching scenes in which Titania simulates having sex with Bottom, who wears a donkey costume during the act.
The 10- and 11-year-olds from the school travelled to see the matinee performance after studying extracts from the play as part of their daily national literacy hour. But by the interval teachers had decided the production "went a bit too far".
Their teacher, Stephen McGaw, said: "What we saw was not what we were expecting. It was sexually explicit and it seemed the director had decided to play the sex card at every opportunity. Everyone knows Shakespeare was a bit cheeky and a bit bawdy, but this went a too far.
"I know the play and I have seen various productions, and this was nothing like I had ever seen before.
"At the interval I called the children together and asked them why they thought I had gathered them together.
"One boy said: `Because it is not suitable for children.' I was relieved they thought that and we left quietly. We didn't make a fuss and we didn't complain.
"The RSC is a wonderful institution and, as an English specialist I admire the wonderful work they do in preserving Shakespeare's works. I just wish they had told us it was a bit near the mark when we booked and we would have simply said `no thank you'."
The school has now asked the company for a refund.
A spokeswoman for the RSC said the company had now written to primary schools warning them that the production was "too adult" for youngsters.
"It is a vibrant, energetic production, which older children and adults will love," she said.
"We obviously sell tickets for all our productions in advance of the opening nights, and often the only information available in advance is details of the design and casting, not the way the play is being performed."