Michael Simpson's son JJ was born 16 weeks early to mum Carla Walker and weighed just 1lb and 9oz.
But thanks to the hard-working NHS staff, his son defied the odds to survive at Nottingham City Hospital's neonatal unit.
Three months on, Simpson, 37, from Boston, Lincolnshire, decided to share the image of his extremely poorly son born on 28 April with a message to the health secretary.
On the photo, Simpson wrote: "Where are you today Jeremy Hunt (Health Secretary)? Bet you're not at work!
"Well there are numerous amazing NHS staff, consultants, doctors and nurses amongst others that are looking after my son and millions of others at weekends and out of hours, get a grip and support them rather than moaning that they don't work weekends.
"Please please like and share this post if you support our amazing NHS staff."
The photo was shared 4,000 times since being uploaded on 19 July.
His wife commented on the photo: "NHS are overworked and underpaid they are miracle workers - that prat needs to give them a break!"
Simpson told the Mirror: "It's taken me a long time to share this picture publicly because of how much it hurts.
"But I was just so angry reading about Jeremy Hunt's comments I had to do something.
"On a weekend, he is probably sitting at home, enjoying time with his family."
Simpson praised the NHS stuff for saving his son's like "so many times" over the last 12 weeks that he has lost count.
Simpson and his wife travel 120 miles to Nottingham every day to see JJ - who is battling chronic lung disease.
He added: "We've seen first hand how hard NHS staff work. They are there all hours of the day and night, seven days a week.
"They are true miracle workers."
Since the photo was uploaded, Simpson has been overwhelmed with the response.
On a recent Facebook post, he wrote: "Didn't realise how much of an impact this would have.
"Thank you to everyone who is sharing this, without the doctors and nurses who have worked tirelessly around the clock seven days a week our precious son wouldn't even be here, NHS staff, you will always hold a special place in our hearts."
The new father later shared a photo of his son, now three months old.
He wrote: "91 days into our journey and I think our little man is beginning to get a little tired too."
Since the comments from Mr Hunt about NHS workers' hours having "tragic consequences", many have taken to social media using the hashtag #ImInWorkJeremy throughout the weekend to prove he is wrong.
HuffPost UK Parents have contacted Jeremy Hunt's office for comment.