In a first-of-its-kind move, the Attorney General, Dominic Grieve, said court papers will be served against a number of individuals who posted the images on the social network site.
Venables was just 10 years old when he and classmate Robert Thompson abducted and murdered two-year-old James Bulger in Liverpool in February 1993.
The pair were jailed for life but released in 2001 under the protection of a court order banning publication of information which could reveal their new identities.
Photographs recently appeared on Twitter claiming to show an adult Venables, now 30, who had his parole revoked in 2010 after admitting downloading child porn.
Breaches of the order may be a contempt of court punishable by a jail sentence or fine, the Attorney General warned.
A statement from the Attorney General's Office said: "There are many different images circulating online claiming to be of Venables or Thompson - potentially innocent individuals may be wrongly identified as being one of the two men and placed in danger.
"The order, and its enforcement, is therefore intended to protect not only Venables and Thompson but also those members of the public who have been incorrectly identified as being one of the two men."
It is the first time the Attorney General has brought contempt proceedings involving the use of social media. However, a number of high-profile cases have seen people fined for breaking the law on Twitter or Facebook.
Nine people have been ordered to pay compensation to the woman raped by footballer Ched Evans for naming her online, while Lord McAlpine is seeking £50,000 in damages in civil proceedings against Sally Bercow over comments she made on Twitter.
Niri Shan, head of media law at law firm Taylor Wessing, said: "Users of Twitter are subject to the same laws of contempt as the mainstream media and publishing a photo of Venables online, in breach of the court order, is clearly contempt of court.
"Knowingly breaching anonymity orders on social media is an action made at the user's own peril. Tweeters charged with contempt should brace themselves for the possibility of fines or imprisonment. These actions are a sign of things to come."
James Bulger's mother Denise Fergus has always opposed the injunction, fearing it could lead to innocent men being accused of being James's killers.
Venables and Thompson abducted James from the Bootle Strand shopping centre in Merseyside before torturing and killing him.
The two boys, who had skipped school, walked James around the streets of Liverpool for more than two miles, stopping occasionally to kick and punch him.
Telling adults who intervened that he was their brother, the pair took him to a nearby railway line and left his body on the tracks in the hope it would be hit by a train.
The toddler had been splattered with blue paint and his battered head lay surrounded by a pile of bricks. His body was found two days later.