The pope's decision, which was confirmed by the Vatican, triggered sharp surprise from the chairman of the Bishops' Conference of France, who termed the situation “unheard of”.
“Monday morning, I handed over my mission to the Holy Father. He spoke of the presumption of innocence and did not accept this resignation,” Barbarin, who has appealed his sentence, said in a statement from his see in the southeastern city of Lyon.
Barbarin said he would remain in Lyon pending his appeal, but added that “for a little while” he would step back from his job, allowing, at the pope's “suggestion”, the local vicar general Yves Baumgarten to run day-to-day affairs.
The 68-year-old is the most senior French cleric caught up in the global paedophilia scandal that has rocked the Catholic Church.
The chairman of the Bishops' Conference, Georges Pontier, told AFP he was “surprised” by the decision.
“I did not expect this scenario which falls between the two most expected,” he said, adding that this “unheard of” situation resulted from the difficulty of “respecting the judicial process” along with the need to “look after the Lyon diocese”.
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On March 7 a Lyon court ruled that Barbarin, a cardinal since 2003, was guilty of failing to report allegations of abuse of boy scouts committed by a priest, Bernard Preynat, in the 1980s and 1990s.
After the ruling, Barbarin said he would go to Rome to tender his resignation.
The pope had previously defended the cardinal, saying in 2016 that his resignation before a trial would be “an error, imprudent”.
Barbarin's lawyer has announced plans to fight the guilty ruling, which was hailed by abuse victims as ushering in a new period of accountability in the French Church.
The case came as the pope seeks to restore faith in the Church following a slew of abuse scandals that have spanned the globe, from Australia to Chile and the United States.
Less than a week after Barbarin's conviction the Vatican's former number three, Australian Cardinal George Pell, was sentenced to six years in prison by a Melbourne court for the “brazen” sexual abuse of two choirboys.