"It is with great pain and regret that I learnt of the recent remarks made by Father Edward Staniek about Pope Francis," Krakow archbishop Marek Jedraszewski said in a statement.
Local media reported Friday that Staniek had delivered a homily last month in which he said: "I pray for wisdom for the pope, for his heart to open up to the Holy Spirit, and if he does not do that, I pray for his quick departure to the House of the Father."
"I can always ask God for a happy death for him, because a happy death is a great grace," he added at a church in Krakow, southern Poland.
Staniek had cited what he viewed as the "pope's erroneous views", including his openness to Muslims, according to local media.
Pope Francis is considered too liberal by many in Poland's church, who still follow the more conservative teachings of Saint John Paul II, the late Polish pope who served from 1978 to 2005.