Anti-bullfighting association Basta said it had lodged a formal complaint with Portugal's National Commission for the Promotion and Protection of Children and Young Peoples' Rights over the Azores incident.
It also called on the local authorities to identify the man carrying the child, thought to be his father.
The pair were said to have been filmed during an annual festival in Casa da Ribeira, a village in the municipality of Santa Cruz where a bull is let loose on the streets tied to a long rope as part of the festivities.
Basta described the incident in a statement as a 'situation of total irresponsibility and a clear violation of the legislation that protects children in Portugal, as well as the United Nations Convention on the Rights of the Child.'
It added: 'The authorities in the Azores should investigate this case and identify the individual who appears in the video.'
The footage emerged as Portuguese lawmakers voted overwhelming against a bill banning bullfights.
An animal rights MP tabled the bill yesterday/on Friday but it received just 31 votes in Portugal's 230-seat parliament.
Unlike in Spain bulls are not killed in the ring in Portugal but out of sight of the public afterwards.
Andre Silva, the politician who tried to get bullfighting banned, said the animals suffered cruelty and suffering 'disguised as cultural heritage.'
Meanwhile in Spain this weekend, four runners were taken to hospital at the start of the famous San Fermin festival — including a Spaniard gored in the bottom.
A 20-year-old Canadian was also among the four men hospitalised.
He was originally thought to have been the second gore victim, although hospital chiefs later confirmed he had a leg injury but had not been gored.
The injury toll was announced shortly after the opening run in the northern Spanish city of Pamplona.
Two of the six fighting bulls became separated from the pack at the start of the half-mile course along the cobbled streets of Pamplona's Old Town.
The animals completed the run in just over two and a half minutes, despite a pile-up in the tunnel leading into the bull ring at the end of the course where a runner fell and several people behind him crashed into him and ended up on the ground.
The San Fermin festival kicked off yesterday at midday with the traditional 'chupinazo'.
Revellers wearing traditional red and white were quickly soaked in sangria as the event got underway.