The Italian national died at HMP Belmarsh, the high security jail in Woolwich, south east London, on Sunday. Details of his death have not been given.
A prison service spokesperson said there would be an independent investigation by the Prisons and Probation Ombudsman.
Brizzi, 50, was found guilty of murdering the 59-year-old at his London flat after arranging to meet for a bondage sex session on dating app Grindr.
The Breaking Bad fanatic - who often wore memorabilia T-shirts to Crystal Meth Anonymous meetings - set about a barbaric plot to dispose of the officer's body, inspired by the TV drama.
Crystal methadone addict Brizzi admitted he was inspired by his favourite TV series Breaking Bad as he tried to dispose of the body of PC Semple by dissolving his flesh in an acid bath.
Police were alerted to the grisly find by neighbours who complained of a terrible smell.
When police searched Brizzi's flat, they found "globules" of flesh floating in the bath, bags containing bones, part of PC Semple's head and pools of human fat in the oven.
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