The theatre had meant to send recordings of its summer schools for children. But the DVDs were reported to have featured explicit sexual content.
The Playhouse said the fault lay with the production company that made the DVDs and that an investigation had begun.
Theatre bosses said the error was only discovered by staff after one of them picked up a copy for themselves and played it. Too bad someone on staff didn't preview the DVD's before sending them out.
The DVDs have since been recalled.
A 10-year-old girl, who had attended a summer stage school at the Playhouse earlier this year, was reported to have been sent the DVD.
Her father described the film as "absolutely disgusting filth".
Some of the children and parents affected have posted messages on social media sites expressing their shock. Many had waited for months for the DVDs.
In a statement, it said: "Edithouse takes full responsibility for the mistakes made in the duplication process of DVD's for the Edinburgh Playhouse, which resulted in highly inappropriate and inaccurate material being sent out to a small number of Edinburgh Playhouse customers.
I'm not sure 'hundreds' qualifies as a 'small number'.
"We would like to apologise sincerely to the Edinburgh Playhouse for the inconvenience and most importantly to the children and parents affected by this terrible error. We are sorry for any distress caused."
It's commendable that Edithouse took full responsibility immediately. It would be much better if they didn't produce pornography DVDs at all.
A Playhouse spokesman said: "We took immediate measures to recall all of the DVDs, sought the advice of the police and notified those affected customers as a matter of urgency. This is all good, but would have been completely unnecessary had someone just bothered to look at one of the DVDs.
"The error occurred at the third party place of manufacture and we have demanded that the DVD production company launches a full investigation into the incident."
Police Scotland said no crime had been committed as this was a production error rather than a deliberate circulation of pornography to youngsters. Not sure I agree with that at all. It's sort of like saying, 'I accidentally raped some little girls'! What do you think? When you accidentally run over someone due to inattention, are you not charged with vehicular manslaughter?
To not charge either the Playhouse or Edithouse with distributing pornography to minors does nothing to ensure it won't happen again. Mind you, the lawsuits that will surely emerge from this may convince them to be more cautious.
When did pornography production become legal anyway? It was a dark day in history!