The musician, 48, best known for hits including Why Does It Always Rain On Me? and Sing, said he was attacked by the animal after he tried to come to its rescue following a car accident.
Healy, who lives in Los Angeles, said the injury was so bad that he was bleeding “all over the shop” and the fire service had to come to his aid.
He wrote on Twitter: “I was driving down my hill and as I rounded a corner there were 3 cars jackknifed and from the middle of the chaos ran a daschund.
“So I jumped out and chased it up the hill. Cars bomb down our hill and it would have been toast.
“So I tried to pick it up and it mauled the shit out my left hand.
“I held on, hoping to chuck it into our porch but then I slipped and it bolted off, leaving me pishing blood all over the shop. So much blood.
“Then all the neighbors came out and one of them called an ambulance.
“I ran into the house and poured alcohol over the wounds… then I came out but it wasn’t an ambulance… it was a massive fire engine… and I have to say, 5 Calvin Klein models got out and then I’m telling them about the daschund and they suggested urgent care…
“By this time there was about 20 cars waiting to pass, I’m pishing blood (by the way ladies and some boys… I totally now get the fireman thing) anyways I drove to Urgent Care on Selma and they cleaned me up good and now I’m here and my finger is patched up and bloody sore.”
He shared photos of a gaping wound on his finger, as well as a shot of his hand bandaged up.
Healy said the dog survived the ordeal and it turned out his owner lives in a home formerly owned by Fleetwood Mac star Stevie Nicks.
He wrote: “The dog… is fine. Was cornered at the bottom of the hill and the owner, who lives in Stevie Nicks old house (pop pickers), was reunited.”