Damien Menzies, 25, attacked the 26-day-old child at a dance show in Deans Community High School in Livingston, West Lothian, on 10 October 2014.
The High Court in Livingston heard how the incident has left the child, who cannot be named for legal reasons, unable to walk or talk.
Medics have been unable to ascertain what effect the injuries will have on the baby’s future life.
They will not know until the baby’s brain is fully developed.
The former soldier was convicted of attempted murder following a trial in June 2016. He had denied harming the child. Sentence had been deferred for the court to obtain reports about Menzie’s character.
On Tuesday, at the High Court in Edinburgh defence solicitor advocate Ian Bryce told judge Lady Scott that Menzies maintained his innocence.
The lawyer also said that the violence for which Menzies was convicted of was “out of character.”
However, passing sentence Lady Scott said she had no other option but to jail him.
She said: “Mr Menzies, you have been found guilty of the crime of attempted murder. The jury found that you acted in a reckless and wicked manner.
“You lost control and you shook a child violently.
“The child’s life is immeasurably reduced. However, the full extent of the child’s injuries are not yet known and will not be known until the child’s brain is fully developed.
“In these circumstances, the sentence of this court will be one of seven-and-a-half years.”
During proceedings, the court heard how the baby had been well and feeding normally before it was taken to a dance show being held at the Deans Community High School in Livingston.
Once at the show, Menzies volunteered to help the child’s mother. He told her that he would change the baby’s nappy.
Less than 15 minutes later, he returned with the tot lying “blue” and “lifeless” in his arms.
Giving evidence, the woman told the court of how the youngster was so limp and floppy that it seemed to have no bones.
She described the baby, now aged around 20 months old, as “still like a newborn with most things.”
Menzies, originally of Bathgate, had denied any wrongdoing.