The spot, created by ad agency DFGW, shows two female players battling it out to win the title until one player cracks and shatters into pieces as she is beaten by her opponent.
The BBC said the trailer was created to convey the physical and mental pressure that the tournament has on a competitor and the idea that Wimbledon is the tournament that makes or breaks players.
The promotion will now no longer be broadcast during children's programming or shows where more than 10% of the audience are typically children.
In a statement, the BBC said: "In response to the feedback we have received, we have taken the trailer out of all children's programmes and programmes for which more than 10% of the audience is children.
"The trailer was not intended to offend or upset anyone and we apologise that it has offended some viewers."
DFGW has worked on a number of BBC sports projects over the last year including six ads for the Six Nations rugby tournament. The agency was also behind work for the Euro 2004 football tournament.
Ofcom said it does not expect material to be shown before the 9pm watershed to intimidate and harm children and welcomed the BBC's action in removing the promotion to a more suitable time where it could not disturb children.
Wimbledon coverage begins on BBC One, BBC Two, BBC Radio Five Live, interactive through BBCi and from June 20 to July 3.
Former Wimbledon champion Jimmy Connors is joining the BBC's commentry team of former champions, along with John McEnroe and three-time winner Boris Becker.
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