Nickolas Wayne Peake, 30, pleaded guilty to aggravated common assault of his five-week-old daughter in September at his family home in Perth.
He was sentenced in the Midland Magistrate's Court on Tuesday to a 10-month community-based order, with programs to help him rehabilitate.
Peake, who has been stood down from the Western Australian Police Force, was woken from his sleep by his crying daughter.
The officer initially tried to give the infant a dummy and cradled her to settle her.
But when she continued to cry, he shook her three times back and forth "after he lost his shit" and said "shut the f*** up".
The child's mother immediately intervened and took the couple's daughter from him.
Peake then left the room and immediately recognised his actions were unacceptable and was remorseful.
The family called a midwife and went to a hospital the following day, where Peake cooperated with medical staff and police after the incident was reported.
The child did not suffer any injuries, and it was not known if her head was supported during the assault.
Magistrate Paul Lyons said it was serious offending and the risk of a catastrophic injury was high.
"It's also serious because of the position of trust you represent in respect to your daughter," he said.
"(It) represents a betrayal of trust to your daughter and your broader family.
"Things could have been far worse than they turned out to be."
The court heard Peake was struggling financially and had been stressed after a violent incident at work and a traumatic birth.
His daughter was also suffering colic and reflux and crying uncontrollably.
Peake and his wife, who was also not named in the court, were getting only a few hours' sleep per night, the court heard.
In sentencing, Magistrate Lyons said the actions were unacceptable and a strong deterrent message must be sent to the community.
He rejected Peake's application for a spent conviction.
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