The 25-year-old mother, who was suffering from post-natal depression, was found guilty of inflicting grievous bodily harm on her daughter, but cleared of attempted murder and causing grievous bodily harm with intent.
Birmingham Crown Court heard that Abdulrahman put her baby daughter in a bin bag and dropped her more than 40ft (12m) down the rubbish chute at a block of flats in Wolverhampton in September 2012.
The baby, who cannot be named for legal reasons, was later found by her father and taken to Birmingham Children's Hospital with serious head injuries.
The court was told the little girl would have gone down the chute at 29mph before hitting a metal plate at the bottom.
Judge Kate Thirlwall said the infant sustained 'catastrophic' head injuries, and would be dependent on other people for help and assistance for the rest of her life.
She said she accepted the incident was not premeditated, and that the mother had been suffering from postnatal depression.
"You will have to live with the consequences for the rest of your life," judge Thirlwall told her.
Abdulrahman had initially denied all three charges made against her, and told the police that her little girl had been kidnapped by strangers.
The prosecution told the court that Abdulrahman deliberately placed her daughter into the chute with the intention of killing her, but she insisted she had not planned the incident, and had 'lost control of her thoughts'.
She said she had been 'tired, sad and exhausted' after her daughter's birth and admitted 'I went to the living room, I put the baby in a rubbish bag and I threw her away'.
"After I had done so, I just couldn't believe what I had just done, and I couldn't understand why I did it. I was in shock," she said.
"I can't tell whether I was crying at the time or not, but I have done this. I wasn't aware of what I was doing.
"If I thought that by doing so I would do some harm to the baby, I wouldn't have done it."
More on Parentdish: Why we must take post-natal depression seriously