Under its current policy, the social media giant prohibits the publication of people's private information, including addresses, phone numbers, identity documents and medical records.
Now, it says it has added "private media" to the list, because the sharing of such material could be used to "harass, intimidate, and reveal the identities of individuals."
"Sharing personal media, such as images or videos, can potentially violate a person's privacy, and may lead to emotional or physical harm," the company said.
Before removing the image or video, Twitter said, it would require a first-person report or a report from an authorized representative to establish whether or not the individual had consented to it being shared.
Once Twitter established that the personal media had been shared without permission, it would then proceed to remove it from the platform, the company said.
It added that the policy changes do not apply when there is public interest at stake, or in an emergency situation.
"This policy is not applicable to media featuring public figures or individuals when media and accompanying Tweet text are shared in the public interest or add value to public discourse," the company said.
The new measures, which went into effect globally on Tuesday, were met with criticism from users arguing that the changes were too immediate, and could result in undue censorship.
The company subsequently clarified the changes in a series of tweets — adding that images and videos showing public events including mass protests and sports events would largely not violate the policy.
"Context matters. Our existing private information policy includes many exceptions in order to enable robust reporting on newsworthy events and conversations that are in the public interest," the company said.