He will also be subjected to hard labour during the sentence
The court heard that Chiluba Jr stole the device from a woman, Ms Brenda Chisha, on September 2, 2017 and traded it for drugs in a notorious slum in Zambia's capital, Lusaka.
Delivering judgement today, Lusaka magistrate Nthandose Chabala said she handed Chiluba Jr a custodial sentence as a deterrence to him and other would-be offenders.
She said she was satisfied that there was enough evidence connecting him to the theft of the phone, and the prosecution had proved its case beyond all reasonable doubt.
Chiluba Snr ruled Zambia from 1991 to 2001. He was dogged by corruption allegations, leading to his immunity from prosecution being lifted after he left office.
He was prosecuted for alleged embezzlement in 2002 but acquitted after a six-year trial.
In 2007, he was convicted of fraud by a London court and ordered to repay $58m in embezzled funds, but the ruling was never enforced in Zambia.