The research, published in the journal Current Biology, also suggests the effect is worse the more often they go to church or mosque.
The study is based on an exercise carried out by more than 1,100 children aged 5-12 around the world.
In it, they were given stickers and asked how many of them they would wish to share with an anonymous person in their school.
The lead author of the study, Dr Jean Decety from the University of Chicago, said it was carried out to test the common view that those with a religious upbringing were 'better' people.
"This view is so deeply embedded that individuals who are not religious can be considered morally suspect, especially in the US."
Dr Decety also has a theory about why children from Christian and Muslim backgrounds appeared less likely to want to share.
It is based on what is known as 'moral licensing'.
"Moral licensing is using something 'good' to justify something 'bad', often without even realising it.
"It is an interesting moral glitch: doing something that helps to strengthen our positive self-image also makes us less worried about the consequences of immoral behaviour, and therefore more likely to make immoral choices."
Dr Decety believes the study's findings corroborate a wider view on piety.
"I hope people begin to see that religion is not a guarantee for morality, and that religion and morality are two different things.
Societies that cultivate secular values are more peaceful and generally 'healthy' than those countries which anchor or base their values on religion."
Christian psychologist Louise Kadayer told Premier's News Hour that true faith in the Lord Jesus is the only thing that transforms behaviour: "We need to look beyond the label of a 'Muslim' family or a 'Christian' family.
"It's definitely about that relationship with Jesus, that relationship with God, that relationship to what we are told to do above all else: love those around us."