The man then continued to deny any wrongdoing after being forced to seek medical help for the distressed youngster, Leeds Crown Court was told this week.
The defendant, who cannot be named in order to protect the identity of the child, finally admitted a charge of actual bodily harm after the incident in Castleford in October 2018.
Outlining the case of the prosecution, Jeremy Hill-Baker told the court that the defendant, who was 26 at the time, had picked the baby up by the arm because he had "inconvenienced" him while he played on his X-Box.
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Despite the obvious pain the child suffered, the court was told the defendant did little to help him until the next day when he finally took him to see a doctor.
The defendant told the doctor that the tot could not move his arm but gave no explanation.
X-rays showed the child was left with a broken humerus, which medical experts said could only have been caused by significant force.
The court was told how the investigation that followed unfairly left another person "under suspicion for a significant time".
The defendant eventually confessed to causing the break, but said it was unintentional.
Christopher Dunn, mitigating for the defendant, said his client had struggled to admit his wrongdoing and described him as an "immature" and a "childish" man who spends his time playing computer games.
But he added: "He richly deserves an immediate custodial sentence, his bag is packed and he is ready to take his medicine.
"He believes he deserves it."
Judge Christopher Batty told him: "Had you deliberately inflicted injury on the child, you would have gone to custody, there is no question about that.
"You did not deliberately inflict the injury but were very, very reckless in your conduct.
"You knew you had hurt him, it must have been apparent by his reaction.
"I accept you feel remorse, but it's a shame it did not manifest itself sooner."
He was given eight months' jail, suspended for 18 months after a pre-sentence review said there was hope for rehabilitation which they claimed he would not receive behind bars.
He was also given 120 hours of unpaid work.