Wesolowski, 67, had suffered from health problems that last month caused postponement of his criminal trial, which was to be the first of its kind initiated by the Vatican against a church official.
Wesolowski had been charged with possessing child pornography in Rome in 2013-14, and the sexual abuse of minors during his 2008-13 stint as the Vatican nuncio, or ambassador, in the Dominican Republic.
He was secretly recalled from his posting in 2012 after the church hierarchy was informed that he had regularly paid young Dominican boys for sexual services.
The disgraced prelate fell ill on the eve of the opening of his July 11 trial.