Tomas Driukas called an ambulance to his Birmingham home just before 1am on 1 April, after the baby – born three months prematurely – started to have breathing difficulties.
Baby Deimante Driukaite was treated in hospital but died a few hours later.
West Midlands Police launched an investigation after it was revealed the baby died as a result of a significant brain trauma consistent with being shaken with force.
She also had bruising to her face and body and 26 fractured ribs after being squeezed.
The 26-year-old denied inflicting the injuries but the jury of eight men and four women took just three hours to find him guilty of murder and two counts of wounding at Birmingham Crown Court.
Detective Sergeant Nick Barnes, from the force’s Homicide Team, said: “Driukas was her father and should have been responsible for the wellbeing and protection of his daughter who was just four and a half months old at the time of her death.
“She was entirely vulnerable, requiring complete care, love and compassion. She was just 55cm tall and weighed less than nine pounds.
“Since the time of her death and the end of the trial Driukas continued to deny any wrongdoing. He has shown no meaningful remorse.
“Even when his daughter was gravely ill he neglected to give an honest account to medical experts in order for them to treat her appropriately.”
Driukas will not be considered for parole for at least 21 years. He received a further nine years for the wounding which will run concurrently.
DS Barnes added: “We would like to thank the numerous medical experts who comprehensively were able to negate the version of events concocted by Driukas as late as November 2015, some seven months after the child died. They were able to provide expert evidence on the true cause of the injuries.
“She had been injured on at least four occasions and had suffered multiple rib fractures caused by her tiny ribcage being squeezed.
“She also had bruising to her face. The force required was well in excess of what would be expected in handling a baby of this size. The cause of her death was non-accidental head injury which had been caused by her being violently shaken.”