Other children held with their parents at Yarl's Wood, near Bedford, were "damaged" by their experience at the centre which was not equipped to deal with these cases, said Anne Owers, the chief inspector of prisons.
When Ms Owers' inspection team reported the autistic child's problems to managers the girl and her family were released.
In a report out today, Ms Owers said: "Our findings ... underline the recommendation we have repeatedly made that the detention of children should be exceptional and there must be independent and immediate welfare and needs assessment of each child."
In May, Ms Owers recommended urgent action to protect children at Scotland's only immigration detention centre, Dungavel House. She said the children's development was at greater risk than ever before. Yet the Home Office failed to implement recommendations made during a visit two years previously.
Today's report found that three children at Yarl's Wood, two of whom were later released, were detained just before their GCSEs, leading Ms Owers to report that education levels were "inadequate" and "depressing."
Yarl's Wood holds up to 900 detainees, including failed asylum-seekers and their families. The centre is run by a private company, GSL UK Ltd.
Detainees were twice as likely to report feeling unsafe than they were at other centres, Ms Owers' team found. And some detainees - particularly African women - reported poor relationships with staff.
Bedfordshire social services department had "very little information" about the circumstances of children there, the report says.
The Home Office said that, since the report, steps had been taken to help children, including improvements to education provision and plans for a dedicated social worker.