Her Instagram post also included a snapshot of her relaxing in a giant, round, marble bathtub while fully clothed.
The post received nearly 4 million "likes" in its first hours online Saturday.
"With you I feel 2 feet small. X 2 @prideofgypsies HAPPY FREAKING BIRTHDAY BABY! An oversized bath tub of happiness for another year of you. #moonofmylifemysunandstars #finallyabathbigenoughtobathadragonin #thenbrokecosispentallmymoneyonbubblebath," Clarke captioned the images.
Momoa turns 40 on Thursday. He is married to actress Lisa Bonet, the mother of his two children.
He and Clarke played husband and wife in Season 1 of Game of Thrones.