The semi-detached property at Llwynhendy near Llanelli would have accommodated three children, aged 11 to 18.
Residents said they feared young offenders would be placed in the house.
The council’s planning committee voted against the plans, despite the authority’s officers recommending it for approval.
The company behind the proposals, Freshstart Care Ltd, had stated that children being homed at the property were already in local authority care, and would not be “accommodating children who are in the justice system”.
The company has declined to comment following the decision earlier.