Fan, who was imprisoned for much of the last two decades and spent his final years under house arrest, died last Sunday at the age of 97 after several days of high fever, according to the US-based Cardinal Kung Foundation, a Roman Catholic organisation.
China has a state-controlled Catholic Church, which rejects the Vatican's authority, as well as an "underground" church. Experts estimate that there are as many as 12 million Catholics in China, split roughly evenly between the two churches.
"He had kept loyal to the Lord throughout his life and endured great suffering. I have great respect for him," she said of Fan, who was appointed bishop of Shanghai in 2000 by Pope John Paul II.
In the square outside the funeral home, a large screen displayed photos of Fan while mourners sang, prayed and listened to a man narrating the bishop's life story.
Chinese authorities had turned down a request from worshippers to hold Fan's funeral service at Shanghai's main Catholic cathedral, the Cardinal Kung Foundation said.
