The new rule is an extension of policies to prohibit "doxxing" - the publishing of private information such as home addresses, without consent.
Critics say the rule is too broad and could be "used to deliberately stifle free expression on the platform".
But Twitter said it would consider the context in which images were posted.
For instance, it would take into consideration whether an image was publicly available, on news websites or "if a particular image and the accompanying tweet text adds value to the public discourse, is being shared in the public interest, or is relevant to the community".
Before removing images or taking enforcement action, Twitter said, it must be notified by the "individuals depicted, or by an authorised representative, that they did not consent to having their private image or video shared".