Mr Dodd was killed in a helicopter crash near Boroughbridge yesterday afternoon.
A candle has been lit for him at the cathedral's ancient altar of St Wilfrid ahead of a service of evening prayer at 6pm.
A spokesman for the Cathedral, in the Anglican Diocese of Leeds, said: “The Dean of Ripon and the whole cathedral community are shocked and saddened to hear of the tragic death of Mr Barry Dodd, the Lord Lieutenant of North Yorkshire.
“Our thoughts and sympathy are with his wife, Frances, and we pray for her as we also pray for the repose of his soul.
“Barry Dodd was a popular and effective Lord Lieutenant of the county, uniting people to work together for the common good, and he was a supportive friend of the cathedral. He will be missed greatly.
“We also pray for Mr Peter Scrope, the Vice Lieutenant, and all the deputy lieutenants as they respond to this tragedy.”
Tributes have flooded in from Yorkshire's business community, the political world and organisations throughout the region.
York City Council said its flag were flying at half mast today in honour of Mr Dodd and his work for the city.
Council leader Ian Gillies said: “Barry will be sorely missed – not only was a close colleague over many years but I had the pleasure of calling him my friend too.
“Barry was well known across Yorkshire and had a great personality. He was a huge support to me during my time as Lord Mayor and he was always very supportive to me and the city.
“My thoughts are with his wife Frances and their family at this incredibly sad time.”