The 78-year-old real estate was sentenced to life in prison without parole on Thursday for the first degree murder of his friend Susan Berman at her Beverly Hills home.
He was found guilty last month of shooting Ms Berman, 55, in the back of the head in December 2000.
A jury also found him guilty of the special circumstances of lying in wait and killing a witness, which in California carries a mandatory life sentence without the possibility of early release.
“All we know he’s tested positive for Covid-19, he’s in hospital and on a ventilator,” his attorney Dick DeGuerin told NBC News.
“He looked awful Thursday, worst I’ve ever seen him. He was having difficulty breathing, he was having difficulty speaking.”
Prosecutors told his trial that Durst killed Ms Berman because she knew too much about the 1982 disappearance of his wife, Kathleen McCormack Durst.
Ms Durst’s body has never been found after she disappeared in New York in 1982 and he has never been charged in connection with her death.
The court was told that Ms Berman had provided a false alibi for Durst in 1982 and that he feared she would reveal that to authorities.
Superior Court Judge Mark Windham, who presided over the trial and sentenced Durst in Los Angeles County on Thursday, described the murder as “awful and disturbing.”
Durst, who appeared at his sentencing in prison uniform, testified in his own defence for 15 days, with prosecutors telling the jury that he had lied or changed his story multiple times.
The trial took place six years after he appeared on the HBO documentary series The Jinx, where he appeared to confess to multiple killings.
During the filming of the show, Durst was caught on a live microphone muttering to himself, “What the hell did I do? Killed them all, of course.”