"I would like to ask all of you for a special prayer for Pope Emeritus Benedict, who, in silence, is sustaining the Church," Francis said in his surprise announcement in Italian at the end of his weekly general audience.
The Vatican said in a statement Benedict had suffered a sudden "worsening" of his health in recent hours. It also said his condition was "under control" and that he was receiving constant medical attention.
Pope Francis urged people to pray for him.
"Remember him, because he is very ill, asking the Lord to console and support him," Francis said.
"Let us remember him. He is very sick, asking the Lord to console and sustain him in this witness of love for the Church, until the end," Francis added, speaking in Italian.
A Vatican source told AFP that Benedict's health began deteriorating "about three days ago".
"It is his vital functions that are failing, including his heart," the source said, adding that no hospitalization is planned, as he has the "necessary medical equipment" at home.
Vatican spokesman Matteo Bruni confirmed Benedict's health had worsened "in the last few hours."
Francis, who visited the former pontiff shortly after his general audience, has often praised Benedict, saying it was like having a grandfather in a home. But the presence of two men dressed in white in the Vatican has at times been troublesome.
Conservatives have looked to the former pope as their standard bearer and some ultra-traditionalists even refused to acknowledge Francis as a legitimate pontiff.
Until a few weeks ago, those who had seen Benedict said his body was very frail but his mind was still sharp.
One of the latest known photographs of Benedict was taken on Dec. 1, when he met the winners of a prize for theologians named after him. He was seated and looked exceptionally weak.
Since his resignation Benedict has been living in a former convent inside the Vatican gardens, with his secretary, Archbishop Georg Ganswein, and a few other aides and medical staff.
Benedict announced his intention to resign on Feb. 11, 2013, shocking a meeting of cardinals. He said he no longer had the physical and mental strength to run the Church.
He formally stepped down on Feb. 28 that year, moving temporarily to the papal summer residence south of Rome while cardinals from around the world came to Rome to choose his successor.
Francis, the first pope from Latin America, was elected to succeed him on March 13, 2013.
Benedict, the first German pope in 1,000 years, was elected on April 19, 2005 to succeed the widely popular Pope John Paul II, who reigned for 27 years.
This article was compiled with data from Reuters and Agence France-Presse.