His mother, Jumarie "Jom" Cadman, was found in hospital and is in a serious but stable condition.
Sydney woman Jom Cadman is in hospital but family members do not know what has happened to her son Julian.
The appeal concluded: "Please share, especially if you have family or friends in Barcelona".
It was still not clear how many people had been involved in the van attack and other incidents on Thursday.
An Australian tourist is missing following a deadly terrorist attack in the heart of Barcelona, the government has confirmed.
The Prime Minister said United Kingdom authorities were "urgently looking into reports" that the child, who has dual British nationality, is missing.
Of the eight Australians impacted by events in Barcelona, Ms Bishop said four were injured, three required consular support and one is unaccounted for.
A spokesperson added that they were "working to find out if any more need our help", and that the number of injured could rise.
Pictured left: Norma Canaveral, who is known as "granny" by Julian Cadman.
Police said they also shot dead on Thursday a man who had driven a vehicle into a police checkpoint in Barcelona, though they had no evidence he was connected with the van attack.
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Authorities in Vic, a small town outside Barcelona, said a van had been found there in connection with the attack.
It quoted the country's Foreign Affairs Minister, Simon Coveney, as saying that the father had suffered knee injuries and the five-year-old boy had a broken femur.
13 people were killed and around 100 injured after a van crashed into a crowd of people in the popular Las Ramblas shopping street.
Julian was born in Britain, but moved to Australia when he was three, the newspaper reports.
The pair, from Sydney, were reportedly in Barcelona for a wedding.
Macedonian officials said one of their citizens was in hospital following the attack, after suffering a broken ankle.
Some 130 people from 34 different nationalities were injured in the attacks, emergency services have revealed. The person had been "in the immediate vicinity" of the attack but was not in any medical danger, they said.
An Italian man, 35-year-old Bruno Gulotta, a father of two, was the first victim to be named.
"He turned up for work this morning, put the radio on and heard about the attack", Mr Bowman said.