Facebook has also offered the family $10,000 in advertising credit.
Seven-week-old Hudson Bond has a form of heart disease called cardiomyopathy and is in desperate need of a heart transplant.
To increase the visibility of his page, Kevin decided to pay $20 for a 'boost' advert to be displayed alongside Facebook user's newsfeeds,
But his advert was rejected by Facebook on the grounds that the photo accompanying it - showing Hudson covered by a blanket and hooked up to the hospital apparatus - was too 'scary, gory or sensational'.
After public outcry over the decision, Facebook's VP of global business communications, Michael Buckley, phoned Kevin to offer an apology.
Yesterday (September 11) Kevin wrote on Facebook:
"Facebook called to offer an apology for refusing Hudson's ad based on his picture. They explained that an automated system accidentally flagged Hudson's photo. They have offered $10,000 worth of Facebook ads to make amends."
He added that he and his fianceé Samantha Stevens had been 'humbled' by the positive response they had received from people around the world.
"Look inside Hudson's room he appears to be stationary. An infant boy tethered to machines, and IV drips," he wrote.
"Yet my little man can move. I'm not talking about raising an arm, Hudson has raised an army."
Hudson is still waiting for a suitable donor heart to be found for him, but Kevin already wants to pass on the support his family are receiving to another ill child - four-year-old Eliza O'Neill who has a metabolism disorder called Sanfilippo Syndrome.
"I met Eliza O'Neill before Hudson was born," Kevin wrote. "She's a remarkable four-year-old girl racing the clock against Sanfilppo Syndrome. A clinical trial that may very well save her life is nearly funded. We've asked Facebook to give $5,000.00 of those ad dollars to her."