In subsequent posts, the company said it aimed to stop images and video being used to “harass, intimidate and reveal the identities of private individuals, which disproportionately impacts women, activists, dissidents, and members of minority communities”.
Street photographer Nick Turpin said he supported efforts to stop online harassment but worried about the impact on those who document the “public realm”.
His work, which is widely exhibited and published, frequently features private people captured in public spaces without obtaining their permission.
Mr Turpin told BBC News many of the images currently on his Twitter feed could violate the policy.
“This new Twitter policy is sudden and shocking,” he said.
“Most of Twitter’s users will live in democracies where what happens in a public place is a matter of public record.
“This is an important principle and many photographers and film-makers that work in the public realm will be immediately affected by this change of policy.
“I can see many like myself abandoning the platform for other services, if we can no longer ‘report’ from the public realm in visual form.”
Twitter said: “Images/videos that show people participating in public events – like large scale protests, sporting events, et cetera – would generally not violate this policy.”
And it “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”.
A public figure could include anyone written about in the press, elected officials and political leaders, celebrities, top executives, news broadcasters and reporters and other public speakers, Twitter said.
The policy would also not apply to individuals who are the subject of public conversations online or offline.
But if the intention was to “harass, intimidate or use fear to silence them, we may remove the content, in line with our policy against abusive behaviour”.
The non-consensual posting of nude images was also already prohibited.
The company added it recognised users may share images or videos of private individuals “in an effort to help someone involved in a crisis situation, such as in the aftermath of a violent event, or as part of a newsworthy event, due to public interest value, and this might outweigh the safety risks to a person”.
But campaign group Big Brother Watch said the policy would be misinterpreted and probably abused.
Legal and policy officer Mark Johnson told BBC News: “Whilst well intentioned, Twitter’s new policy is badly written and overly broad.
“It will inevitably result in vast swathes of censorship online.
“This new rule will be abused and used to deliberately stifle free expression on the platform.”