Julian Cadman became separated from his seriously injured mother Jom during the panic and confusion on Las Ramblas on Friday.
At least 100 people were injured and more than a dozen killed in the Spanish city when terrorists used a van to run down pedestrians on the tourist thoroughfare.
The mother and son from Sydney were in Spain for a wedding this weekend.
Ms Cadman's husband Andrew has flown to Barcelona to search for his son.
Addressing the Tasmanian Liberal Party Conference on Saturday, Mr Turnbull spoke of the anguish the boy's family would be suffering.
"I think we should all, in a our quiet moments, say a prayer for that little boy," Mr Turnbull said.
"All of us as parents know the anguish his father is going through and his whole family is going through, as they rush to seek to find him in Barcelona."
Ms Cadman's father-in-law, Tony Cadman, says she is in a serious but stable condition in hospital, but his grandson is missing.
"Julian is seven-years-old and was out with Jom when they were separated, due to the recent terrorist activity," he said in a Facebook post.
Another Sydney woman, Suria Intan, who was on the last few days of a European holiday with friends, is also in a serious condition in hospital.
Ms Intan, a Commonwealth Bank worker, is heavily involved with the Hillsong Church.
A Hillsong spokesperson told AAP its church in Barcelona is supporting her and her family.
Foreign Minister Julie Bishop said four Australians were injured in the attack, targeting tourists.
Two Victorian men were hit by the van, but have been released from hospital.
During his speech in Tasmania, Mr Turnbull said he would soon release Australia's first national strategy for protecting crowded places from terrorism, citing the Spanish attack as an example.
The counter-terrorism document will be given to Australian businesses and councils, outlining ways to prevent vehicle attacks.
"We have to constantly stay ahead of our enemies in this regard," Mr Turnbull said.
