The former church handyman reportedly fell ill in his cell at Edinburgh's Saughton Prison on Sunday afternoon.
He is said to have been taken to the city's Royal Infirmary by ambulance.
A spokesperson for the Scottish Prison Service said: "We can confirm that a 69-year-old prisoner from HMP Edinburgh was taken to hospital yesterday."
An eye witness claims to have seen the murderer being wheeled into the hospital by a medic and still handcuffed to a prison officer.
Tobin is currently serving a life sentence for raping and murdering Polish student Angelika Kluk, 23, and hiding her body under the floor of St Patrick's church in Glasgow, where he was working as a handyman, back in 2006.
He has also been convicted of murdering 15-year-old schoolgirl Vicky Hamilton, of Redding, near Falkirk, in 1991, and 18-year-old Dinah McNicol in the same year.
Last year, he was taken to hospital after being attacked in prison.