Jack and Anna Peckitt, who run Cuckavelda Gundogs near Ampleforth, said 11 Labradors and two cocker spaniels had died after a tree blew down during Storm Dudley on Wednesday.
It took down a power line meaning wires with a voltage of 11,000 fell onto the kennel block and electrified the runs.
A statement read: "It is with a heavy heart we would like you to know Cuckavalda Gundogs have had a tragic accident around 4pm yesterday.
"A tree blow down taking a powerline of 11k vol with it which fell on the kennel block, with electrified the runs. Unfortunately 13 dogs lost their lives.
"A full investigation is underway by Northern Power Grid.
"Jack, Anna and Tom would like to thank everyone who have shown their concern and given help. And to Grace Lane Vets for coming out.
"At this time there is so much to do and things to sort so we ask that you do not telephone.This photo was taken only last week and very few of the black Labradors are still with us.
"We remember Troy, Olive, Guy, Goldie, Port, Dill, Dora, Rick, Cora, Polly, Tilly, Ivy and Rose. RIP you beautiful creatures - all taken far too young. Aged between seven months and six years."
Around 680 households in the North York Moors area were left without power for several hours due to the incident.