Gilbert Corette, 45, admitted the manslaughter of his mother, 81-year-old Florise Corette, last month.
He also admitted causing grievous bodily harm to his sister on the grounds of diminished responsibility.
The judge said it was a "terribly sad and tragic case".
Corette, of Manor Avenue, Brockley, south London, was given a hospital order and restriction order with no time limit to protect the public.
The Old Bailey heard he was diagnosed with a depressive condition and Asperger's syndrome in 2010.
The court was told the supermarket shelf-stacker was sectioned in March 2015 and admitted to Ladywell Unit located at Lewisham Hospital.
The specialist unit for patients with mental health disorders is managed by South London and Maudsley NHS Foundation Trust.
In July his condition and behaviour was judged to have become more stable and he was allowed to go unescorted to his mother's home in Lochaber Road on day release.
Later that day he refused to return to hospital and said he feared his life was in danger.
The court heard he picked up a champagne bottle and hit his sister, saying he "had to do it".
He then went downstairs and attacked his mother, who was frightened of him and had padlocked some of the rooms.
A post-mortem examination found she died of head injuries.
Judge Wide said he was satisfied the defendant was suffering from a mental disorder.
A family statement said: "The last nine months have been an incredibly difficult time for all of us, but we welcome the sentence of the court so that now Gilbert can get the full care and treatment he deserves.
"We have serious concerns and questions about how he came to be released when clearly unwell, on the day he killed our mother, and will await the forthcoming NHS investigation with interest.
"We sincerely hope that it makes a real difference, so that tragedies like this can never happen to any other family in London ever again."
South London and Maudsley NHS Foundation Trust said: "We offer our full condolences to the family in this tragic case. We have carried out a thorough internal investigation into the care and treatment of Mr Gilbert Corette and shared this with his family."
It said it was also involved with an ongoing domestic homicide review into the death and would not comment further until the review was published.
A man who killed his mother with a champagne bottle hours after being discharged from a mental health unit has been handed an indefinite hospital order.