The council failed to properly identify the needs of the boy, who also has social and communication difficulties.
Ombudsman Nick Bennett's report said the boy endured a "lengthy period" without receiving appropriate education because of the council.
Wrexham council said it accepted the ombudsman's recommendations.
Mr Bennett's report, published on Friday, said: "I'm extremely concerned that this pupil did not receive the support that he needed and the deep upset this has caused the child's family.
"The fragmented approach to this child's education is simply not good enough and I believe in this case he has been let down by the system in place."
The boy's mother told the BBC: "It was clear right from the offset, from starting in mainstream education, that he was struggling.
"I think it's often quite easy to blame either the parents or the child and to assume that they are the ones with the problem and this is something that needs to be addressed by the family itself.
"A lot of it is angled in that way and without any appropriate level of support."
Wrexham council had "placed the onus" on schools in its area to pursue "alternatives" to the statutory assessment usually undertaken for people who might need support for special education needs (SEN), the report said.
In this case, it issued a form of school-based provision called an Extended Action Plus Agreement (ESAP), which was not recognised in the council's procedures or policies and "should not have been used as an alternative".
The council has agreed to apologise to his mother and to pay for failings identified in its complaints handling.
The ombudsman recommended the authority carry out an independent review of the case, review its policy and audit any other ESAP agreements.
Wrexham councillor Michael Williams, lead member for education and children's services, said: "We are pleased to see that the ombudsman's report notes we have already taken steps to apologise to the lady involved, and also recognises the restructuring of our complaints process so as to avoid those issues which were raised in future.
"We will also review our existing ESAP arrangements in order to find whether further educational support, or re-categorising pupils on ESAP to SEN, is necessary."
A visually-impaired schoolboy was "let down" by the education department at Wrexham council, the public services ombudsman for Wales has said.