The notorious serial killer was in hospital with suspected heart problems but returned to HMP Frankland on Tuesday after five nights away.
He developed symptoms on Thursday and medics at the top security jail in County Durham and is now in isolation.
The 74-year-old has underlying health issues and a source told the Sun: “He ticks so many of the danger categories for coronavirus.”
Sutcliffe, who is currently serving a whole life order after being convicted in 1981 of murdering 13 women and trying to kill seven others, is said to be stable.
The source added: “He started showing symptoms on Thursday. The results were turned around quickly because of the danger of him spreading it.
“The worry for him is that he ticks so many of the danger categories for coronavirus.”