Philip, 97, walked away unhurt after his Land Rover overturned in the incident - which also involved a Kia car - on the A149 on Thursday afternoon.
Dr John Sentamu also prayed for people traveling in a second vehicle. A driver and her female passenger required hospital treatment.
The Anglican leader tweeted: "Almighty God, the Fountain of all Goodness, we humbly beseech thee to bless Philip Duke of Edinburgh.
"Endue him with thy Holy Spirit, enrich him with thy Heavenly Grace, prosper him with all happiness and bring him to thine everlasting kingdom, through Jesus Christ our Lord."
One witness described Philip's vehicle "turning on its side over and over".
Roy Warne, 75, told The Sun: "It was frightening to see a powerful car rolling like that.
Almighty God, the Fountain of all Goodness,We humbly beseech thee to bless Philip Duke of Edinburgh:Endue him with thy Holy Spirit; enrich him with thy Heavenly Grace; prosper him with all happiness; and bring him to thine everlasting kingdom, through Jesus Christ our Lord. Amen.— John Sentamu (@JohnSentamu) January 17, 2019
"I rushed to the other car - there was smoke coming out as if it may explode."
The crash took place at the Babingley crossroads between King's lynn and the north coast of Norfolk.
Concerns have been raised in the past about road safety on the A149 near Sandringham.
Coincidentally, the county council is due to meet on Friday to discuss proposals to cut the speed limit on the road to 50mph and install safety cameras.
God of Love and Compassion reach out with your Peace to the people who were in the car involved in the traffic accident with Prince Philip's vehicle.Amen.— John Sentamu (@JohnSentamu) January 17, 2019
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