Tobin, 65, serving three life sentences for the murders of Vicky Hamilton, Angelika Kluk and Dinah McNicol, became ill at Edinburgh's Saughton Prison.
The killer was reportedly taken to the city's Royal Infirmary.
He suffered chest pains and collapsed, unable to breathe, it was reported.
It is understood he has now returned to the prison.
Tobin is certain to spend the rest of his life behind bars. The serial killer is serving a life sentence for raping and murdering Polish student Angelika, 23, and hiding her body under the floor of a Glasgow church in 2006. He has also been convicted of murdering 15-year-old schoolgirl Vicky, of Redding, near Falkirk, in 1991, and 18-year-old Dinah in the same year.
Their bodies were found 17 years later, buried in the garden of his former home in Margate, Kent.
Police have examined hundreds of other unsolved murder cases to see if they could be linked to Tobin.
Detectives also looked at possible links between the killer and the Bible John murders in Glasgow between 1968 and 1969. Three women, Patricia Docker, 25, Jemima McDonald, 32 and Helen Puttock, 29, were all murdered.
However, although it is thought Tobin lived in the city at the time, any link between him and Bible John has never been established