"This may look like a blurry shi**y iPhone pic but here's what it actually is: an image of my father on his zillionth ER trip of the year with me last month, checking to make sure no one came into the room who didn't need to," the Girls creator wrote.
Dunham was recently hospitalised after suffering from a sever case of endometriosis.
"This man has been with me day and night: as I slept after surgery, as I was wheeled into an MRI, as I lay abject and feeling sorry for myself. He made friends with every nurse. When I got home he blended banana shakes when I wouldn't eat, woke me up with my meds at 3am and made me laugh every day."
Dunham, 31, also went on to mention her father prioritised caring for his daughter over living "his own busy life."
"I'm healthy and safe because of his unyielding love. On this Father's Day I want to celebrate all the men who defy the signals culture sends them and nurture, nurture, nurture. I love you Papa. You're my best friend," she wrote.