Sharif was sentenced in absentia to 10 years in prison and fined 8 million ($10.5 million pounds; €8.9 million), his daughter was handed an 8-year term and ordered to pay 2 million pounds, while his son-in-law, Muhammad Safdar, was given a one-year prison sentence.
Maryam Aurangzeb, a spokeswoman for the ruling Pakistan Muslim League party, says the appeal was filed Monday with the Islamabad High Court.
"PML-N united under leadership of Nawaz Sharif", she said while talking to mediamen at flower market Banni Chowk.
On July 13, both Nawaz and Maryam were arrested at Lahore airport on their arrival from London and sent to Adiala Jail, Rawalpindi, to serve their sentence.
Nawaz Sharif in an interview to media persons on Friday from Abu Dhabi airport said he is fighting to restore democracy in Pakistan and bring in revolutionary changes in the present system.
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"The elections are being contested in an environment of fear", Pakistan People's Party chairman Bilawal Bhutto Zardari said.
"Nawaz Sharif has been arrested on corruption charges". The main allegations against the PML-N leaders include damaging public buildings and properties, threatening and injuring the law enforcement agencies officials.
"This FIR is just another attempt of intimidation and political victimisation", Malik said.
The father-daughter duo was in London to meet Sharif's ailing wife Kulsoom Nawaz, who is undergoing treatment for cancer.
Sharif's return comes at a time of dwindling fortunes for his party, which a year ago was considered a run-away favourite to retain power.
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Sharif was ordered jailed after failing to explain how the family acquired the London flats in a case stemming from 2016 Panama Papers revelations that showed they owned the apartments through off-shore companies.
Mr Shahbaz, who is also president of Pakistan Muslims League-Nawaz, went on to highlight the conditions faced by the former prime minister in jail.
After the Supreme Court ousted Sharif last July, the courts barred him from heading the PML-N party he founded.
A appeal was also filed against conducting the proceedings of the remaining two corruption cases within the Adiala jail premises, it added.
Violence has escalated in the run-up to the balloting, with horrific attacks over the weekend killing 153 people, including a provincial assembly candidate during an election rally in southwestern Baluchistan province. Khan's Tehrik-e-Insaf party also has high expectations of winning the vote and having him become the next prime minister.
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