According to the Daily Mail, 43 people contacted the organisation complaining about an "overtly sexy scene" in the last show.
In the episode, companion Amy Pond (Karen Gillan) kisses the Doctor (Matt Smith) and tries to undress him.
She also teases him about how long ago he last had sex and suggests that she would not mind having a one-night stand.
Vivienne Pattison from Mediawatch UK said: "I have to say the scene was slightly out of place in a children's programme. I thought it sailed pretty close to the wind."
A BBC spokesperson confirmed that 43 complaints had been received but said: "Millions of Doctor Who fans watched and enjoyed last Saturday's episode, including the lighthearted and humorous scene in which Amy kissed the Doctor."
Doctor Who continues on Saturday at 6pm on BBC One.