At the same time, he praised the generosity of "ordinary people" in the northern Italian metropolis.
This emerges from an interview with the daily newspaper "Corriere della Sera" published on Friday.
Delpini said: "I am often amazed by people's willingness to donate to the pastoral, cultural and charitable activities of the local church. I often have to thank ordinary people. (...) But I worry about the rich. There are so many wealthy people in Milan who don't use their riches to do good. Don't they really have a soul they want to save?"
"Too great a social divide"
Commenting on Milan's current development, he explained that the city was in danger of only being attractive to tourists, business people, construction companies and investment funds; normal people could hardly afford to live there.
There is too great a social divide.
With around seven million inhabitants and home to numerous companies, the greater Milan area is the wealthiest metropolitan region in Italy.
With 4.9 million Catholics, the Archdiocese of Milan is the largest diocese in Europe.
Delpini (74) has been in office there since 2017.