Angelo Jurado-Marmolejo was reported missing by his mother, Karol Marmolejo, who he lives with full-time in the Whitehall area of Bristol, on March 2.
Avon and Somerset Police said Angelo's father, Rafael Jurado-Cabello, 43, did not return him home following a pre-arranged visit.
Mr Jurado-Cabello, a Spanish national, is in breach of a court order and wanted on suspicion of child abduction.
Detective Inspector Matt Lloyd said: "Our immediate priority is to locate Angelo and do all we can to ensure he is safely returned to his home in Bristol.
"Mr Jurado-Cabello in is breach of a court order put in place to protect Angelo's welfare.
"This will be an extremely unsettling experience for Angelo as he's been taken away from his family home, his primary school and his friends.
"We believe Rafael Jurado-Cabello may have taken Angelo abroad and we're making further inquiries with the Spanish authorities to locate him as soon as possible."
Mr Jurado-Cabello is described as white, between 5ft 6in and 5ft 7in, and with black hair.
Angelo is white with short wavy dark brown hair, dark brown eyes and is 4ft 4in.
He was last seen wearing a zip-up fleece, dark trousers, red trainers and carrying a blue rucksack.
Anyone who sees father or son is asked to call 999 giving the reference 5219046310.
Angelo's mother said she and his elder brother David were "desperate" to have him home, describing the schoolboy as "our treasure".
"We miss the morning cuddles he asks for every day. Angelo will be missing his family, his friends and his school, and we are very worried about him," she said.
"Angelo often has a smile on his face, as he is a very lively person. He wants all the people who are next to him be having fun too.
"Angelo enjoys having a lot of family time - at the park, playing board games, at home, and is very sociable too - he is always busy.
"Angelo is more aware now of his situation, where he lives and his surroundings, despite his young age.
"Angelo is comfortable showing his emotions, happiness, sadness and can shed a tear after watching a film. He will also try to explain if he is not happy though."
She described her son as an active person with "endless amounts of energy", whose biggest passion is football.
Angelo supports both Juventus and Real Madrid and his favourite player is Cristiano Ronaldo.
"He is determined to become a football player one day, he trains every week with his team, and has become a very confident player," she said.
"He has extra coaching and can be seen playing football at the local park with his brother and mum several times a week.
"Angelo is bi-lingual, belongs to the school football club, trains in Taekwondo and is a bit of a daredevil at heart."
She said the family had "no information" about where Angelo may be and asked anyone with information to contact police "as soon as possible".
Anyone who has spoken to or been in contact with Mr Jurado-Cabello since March 2, or has information about where he and Angelo may be, should call 101.
Those abroad with information should call +44 1275 849996, Guardia Civil on +34 696 911659, or contact Avon and Somerset Police online.
By Claire Hayhurst, Press Association