Traherne Williams shook three-month-old Sophia Williams and threw her onto a couch at his home in Broxburn, West Lothian on 30 May 2016.
Sophia then became unresponsive and was taken to hospital but died from her injuries on 5 June.
She suffered “significant brain damage”, police said.
Williams, 23, pleaded guilty to culpable homicide on 4 May – which is defined as causing loss of life through wrongful conduct, but where there was no intention to kill or wicked recklessness.
In his sentencing statement, published online by the Judiciary of Scotland, judge Lord Matthews said: “Parenthood is an enormous privilege but it carries with it enormous responsibilities of nurturing, care and protection.
“As a child grows older the nature of the responsibilities will change but any sane person who is old enough to be a parent knows that a babe in arms is a delicate creature who requires to be handled with the greatest of care and patience.
“Instead of displaying these qualities when she cried, you became frustrated through a combination of circumstances and threw this defenceless child, your own flesh and blood, onto a sofa and in so doing you brought about the catastrophic chain of events which led to her death before she had had any real chance of enjoying the gift of life which you had helped to give her.
“As you appreciate, while this act was the work of moments and was not a prolonged assault or a premeditated killing, only a custodial sentence is appropriate for this type of crime.”
Detective chief inspector Rory Hamilton said: “The injuries inflicted upon Sophia Williams by her father left her with significant brain damage from which she could not recover.
“Traherne Williams was in charge of his daughter’s care and well-being and his despicable actions robbed her of her future.
“I would like to thank Sophia’s extended family for their support and co-operation and it is my sincere hope that the sentence handed to Williams offers them some form of closure so that they may begin to move on with their lives.”