The Auckland man, who has interim name suppression, was accused of assaulting his son which caused a massive and fatal brain bleed.
His defence, led by Rachael Reed, QC, had argued the 11-month-old's death was "a dreadful and highly unusual accident" and the baby fell while his father was out of the room.
Reed foreshadowed an application for permanent name suppression for her client, which will be dealt with at a later date.
The jury had deliberated for three days but was unable to decide whether the man was guilty of manslaughter after the boy died in December 2017.
The man was supported in court by his wife and parents throughout the case.
During the trial the defence said the man heard a thud and went back into the living room to find his son crying and holding a pair of red headphones, which had been on the couch.
Reed said the man then put his son - he and his wife's first-born after numerous rounds of IVF - in a jumper where he could keep an eye on him from the bathroom.
But when he looked back, his son's head was slumped to the side.
The court heard the man's call to Plunket, a number which he'd saved to his phone.
"I'm not sure what's happening with my boy ... He's gone completely floppy," he told the operator in a panic.
"Come on buddy. Come on buddy, come on. You're okay. Come on, wake up," he could be heard saying to his son.
"Oh my God, he's so stiff, he's so stiff."
Police spent a year investigating the baby's death and even bugged the man's apartment, phones and car to try find evidence of a cover-up.
However, police failed to uncover anything.
During his interview with police - the day after his son's funeral - the man said he was confused as the investigating officers about what happened to his son.
"I don't understand what has happened," he told police.
"I want to find out what has happened more than you. He's my son and he's passed away and I want to know why."
He said his son was a lovely, smiley boy who was perfect in every way.
"I wouldn't hurt [him]. The thought wouldn't even cross my mind. He was not something that was easy to get, as I've told you."
The baby had no historical injuries and there was no history of family violence, Reed said.