The ad, which appeared in the area where Baby P lived and died, showed a picture of Steven Barker with accompanying text stating: "Steven Barker: Animal Abuser, Baby Abuser, Rapist. People who are violent towards animals rarely stop there."
The Advertising Standards Authority banned the ad on the grounds that it could "cause serious offence and distress to some residents".
Barker was jailed for 12 years in November 2008 for causing or allowing the baby's death, and was also jailed for life with a minimum term of 10 years for raping a different child.
The ASA upheld a single complaint that the ad was offensive and distressing, used unnecessary shock tactics and exploited the death of Baby P. It also said that the ad, because of its location, was particularly offensive and distressing to residents of that area.
The ASA overruled PETA's argument that people who abuse animals when they are young often go on to commit violence against fellow humans.
In a statement, PETA said: "The American Psychiatric Association identifies cruelty to animals as a diagnostic criterion for conduct disorders, and the US Federal Bureau of Investigation uses reports of crimes against animals in analysing the threat potential of suspected and known criminals."
PETA argued that the ad's message is potentially lifesaving and too important to ignore. The organisation said that the ad also appeared in a location in Wales where cats had been poisoned.
It had hoped to use the ad across the UK. However, the ASA ruled that it cannot appear again in its current form.