The Cardinal heralded as the man who could be the first black Pope has said sex abuse could not happen in Africa, on the same scale as Europe, because of tough anti-homosexuality laws.
Survivors of abuse by priests say they "fear for the safety of kids in Turkson's diocese if he denies there are predatory priests there".
Cardinal Turkson is currently the second favourite to be the next pontiff, and had been championed by progressives who have urged the Vatican to elect the first African pope.
Cardinal Angelo Scola of Milan is currently favourite to succeed Benedict XVI.
In an interview with CNN, when asked about whether it was possible the Catholic sex abuse scandal could happen in Africa, the cardinal said it would not happen, "to the same extent or proportion as we have seen in Europe"
He continued: "African traditional systems kind of protect or have protected its population against this tendency.
“Because in several communities, in several cultures in Africa homosexuality or for that matter any affair between two sexes of the same kind, are not countenanced in our society.
"So that cultural taboo, that tradition has been there. It has served to keep it out.”
He also defended the ban on any women ministry in the Church, saying: "If one does not have access to ordination, it is not discrimination. It is just how the church has understood this order of ministry to be.”
The Survivors Network of those Abused by Priests said in a statement: “To say that Cardinal Peter Turkson’s claims about clergy abuse in Africa are uninformed would be far too kind. We hope this awful comment disqualifies him from consideration as the next pope.
"We hear less about clergy sex crimes and cover ups in Africa for the same reasons we do throughout the developing world: there tends to be lesser funding for law enforcement, less vigorous civil justice systems, less independent journalism, and an even greater power and wealth difference between church officials and their congregants."
The group continued: " Not only is the link between homosexuality and child abuse a fallacy, but it is a weak shield to hide behind.
"It's hard to address a crisis you don't think exists. So we fear for the safety of kids in Turkson's diocese if he denies there are predatory priests there.
"It’s far more likely that Turkson’s brother bishops in Africa have been involved in covering up clergy sex abuse crimes just like their colleagues across the globe. To pretend that Turkson’s home is devoid of the problem is erroneous, and offensive to still-suffering victims in Africa.”
Homosexuality is a crime in 37 countries in Africa. Most high profile is Uganda, where members of parliament are still fighting to introduce the death penalty for gay people.
Cardinal Turkson said he believed it was certainly possible for a non-European pope to be chosen: "It is certainly possible to have a Cardinal come from the Southern part of the globe.
"There are churchmen from there certainly capable of exercising leadership.
Asked by CNN's Christaine Amanpour about how the church could stay relevant in the modern world if it remained anti-homosexual and rejected women priests, he said: "We need to be true and faithful to the faith, and we need to be relevant to the society to which we preach our faith.
"We may not sacrifice one for the other. We seek to be relevant to society and meet the needs of humankind, we also need to be mindful of what it is that a church believes.
"Do you know where I am going? Otherwise we cease to be a church."
It is not the first time the Cardinal has voiced controversial views about homosexuality. Last year, the National Catholic Register reported the Cardinal saying it is important people understand the ‘reasons’ why some African governments have created legislation against homosexuality.
Turkson argues the ‘intensity of the reaction is probably commensurate with tradition’, saying the African culture needs to be respected.
‘When you’re talking about what’s called “an alternative lifestyle”, are those human rights?’ he said.
‘There’s a subtle distinction between morality and human rights, and that’s what needs to be clarified.’
The other Pope potential from Africa, Nigerian Cardinal Francis Arinze likened homosexuality with pornography, infanticide and adultery in a 2003 speech at Georgetown University.