Professor Wendy Savage, a voting member of the British Medical Association Council, made the controversial comments in an interview with the Mail on Sunday.
Prof Savage, a women's rights campaigner and retired obstetrician and gynaecologist, was speaking after a proposal to decriminalise terminations passed the first hurdle in the House of Commons last week.
Her intervention is likely to spark a strong reaction from campaigners on both sides of the argument.
Prof Savage said sex-selective abortions were a "myth" but said women should still have the right to choose if that is what they wanted.
Parents wanting to find out the sex of their baby can usually do so in a mid-term scan at between 18 to 21 weeks but some hospitals have a policy of not telling, according to the NHS Choices website.
Prof Savage, speaking in a personal capacity, told the paper: "Because of this sort of anxiety some places won't tell the woman the sex of the foetus, which is outrageous.
"It's her body and her foetus, so she should have that information.
"If a woman does not want to have a foetus who is one sex or the other, forcing her (to go through with the pregnancy) is not going to be good for the eventual child, and it's not going to be good for (the mother's) mental health."
Under current laws, it is illegal for a woman to have an abortion after 24 weeks for non-medical reasons and each procedure must be signed off by two doctors before it can go ahead.
But Prof Savage said in her experience she only had a "couple" of cases over more than 24 weeks.
She added: "It is a woman's right to decide. It's her body. She is the one taking the risks.
"The foetus is a potential human life at that stage (in the womb); it is not an actual human life ... I think you've got to concentrate on the (rights of the) woman."
Conservative MP Mark Field slammed the suggestion that sex-selective abortion could be allowed.
He told the paper: "Suggesting that women should be able to abort babies solely because they happen to be either male or, much more usually, female, is utterly abhorrent."
MPs last week voted in favour of the Reproductive Health (Access to Terminations) Bill, which would remove criminal sanctions for women and doctors in England and Wales and place regulation with professional bodies.
But Christian MP Maria Caulfield warned the change could bring about a rise in "back street abortions".
A BMA spokeswoman said: "The BMA supports the current law on abortion.
"Though we recognise the diversity of opinion amongst membership, we advise members to act within the boundaries of the law and their own conscience.
"Given the range of views on this subject, patients must be entitled to impartial and objective medical advice and treatment."