From The BBC: The on-screen caption featured an animated cartoon of presenter Graham Norton, host of Over the Rainbow.
It appeared as The Doctor, played by Matt Smith, was making an emotional speech during the story's cliffhanger ending for The Time of Angels.
The trailer was seen by millions of viewers watching on BBC One in England.
Fans have also been complaining on social networking site Twitter. One wrote: "Why is the BBC treating its audience like idiots?"
Another said: "Don't blink or Graham Norton will catch you."
The BBC often promotes programmes in this way but the corporation has acknowledged that in this case the scheduling was inappropriate.
A BBC spokesman said: "We apologise for the timing of Saturday night's trail."