Dame Judi, whose marriage to fellow actor Mr Williams is one of the closest and most enduring in showbusiness, abandoned her starring role as the ageing actress Esme Allen in Amy's View to return to England.
She was anxious to be at her husband's bedside after he was diagnosed with the illness, an inflammation of the lungs that is not generally life- threatening.
Dame Judi, who won the Tony for her portrayal of Esme, missed Wednesday night's performance and flew home on Thursday. She said in a statement yesterday: "I am devastated to disappoint anyone who came to see me, but because of the circumstances I am unable to perform."
The National Theatre in London, where Mr Williams performed in Russian playwright Alexander Ostrovsky's The Forest earlier this year, confirmed that he was ill and said Dame Judi's date of return to New York was uncertain.
Genista McIntosh, the theatre's executive director, said: "Everyone at the National was very sorry to hear Michael was ill and that Judi has had to come back. We all wish him a speedy recovery."
The couple, both aged 63 and who live in Hampstead, north London, have a famously happy marriage and celebrated their 28th wedding anniversary earlier this year.
Although Dame Judi - who also won an Oscar this year, for her role as Queen Elizabeth I in the romantic comedy Shakespeare In Love - is far better known than her husband, he is a celebrated actor in his own right.
Mr Williams, whose stage experience includes 14 years with the Royal Shakespeare Company, has supported his wife through a series of high-profile roles in film and theatre while pursuing his own successful career. He has played all of the major Shakespearean roles, and worked with directors including Peter Hall and Peter Brook.
Mr Williams co-starred with Dame Judi in the Eighties hit television series A Fine Romance, and they also appeared together in the West End play Mr and Mrs Nobody. Mr Williams was in the television drama September Song with Russ Abbot and, more recently, in the Granada sitcom Conjugal Rites.
The couple, who have a daughter, the actress Finty Williams, manage to spend a lot of time together despite their schedules. They are united by, among other things, religious faith; Mr Williams is a devout Roman Catholic and Dame Judi, a devout Quaker.
They married in their mid-30s, after meeting nine years earlier over a cup of tea. Dame Judi had just finished a relationship with Leonard Rossiter and Mr Williams was single.
Despite the length of their marriage, they still indulge in romantic gestures. Mr Williams sends Dame Judi a single red rose every Friday.
He said in an interview last year: "When we married, we went through a sacrament of marriage. I know it's a bit old-fashioned these days, but I was brought up to believe that if you made a vow, particularly in those circumstances, you kept it.
"Of course, one is only human and there have been temptations along the way, but ... I know there's not much point in going after second-best when you've already got the best.
"Jude is the most stunning lady I have ever met and I adore her as much today as the day I married her."Reuse content