Sharif, 67, resigned during his third stint as prime minister after the Supreme Court ruled on July 28 that he should be disqualified and ordered a criminal probe into his family over allegations stemming from the "Panama Papers" leaks of global offshore companies.
Before leaving Gujranwala, in a meeting with leadership of PML-N, Nawaz Sharif stated that he was not given justice by Supreme Court.
Sharif also demanded accountability from military dictators and judges who he said have been sending prime ministers packing home in the last 70 years.
The former premier is now leading a procession from Islamabad to Lahore, the capital of Punjab province and the PML-N's seat of power.
Last month, Sharif was disqualified by a five-member Supreme Court bench for dishonesty.
A defiant Nawaz Sharif criticised on Thursday the judiciary for forcing him to quit as prime minister, saying it was an "insult" to 200 million people of Pakistan that their elected leader was unceremoniously ousted with a single stroke of pen.
Nomination papers for Begum Kulsoom Nawaz were submitted in the eastern city of Lahore by her son-in-law, an official from Sharif's eponymous Pakistan Muslim League-Nawaz (PML-N) told AFP.
Thousands of PML-N supporters thronged the GT Road to express solidarity and love for their ousted leader whereas camps have also been formed all along the way.
Rashid further said that the PML-N was being "forced" to contest the by-election due to Nawaz's ouster, adding that they should do so on a level playing field without using government machinery.
"They have only removed me on paper but they have not removed me from your hearts". "If I was corrupt then I would have been ashamed", he said.
"I am going home and I do not want you to get me restored".
Sharif said that every time the country is pulled back when it reaches at a takeoff stage.
Addressing a huge crowd in Gujranwala, he asked the people if they accepted the court decision against him and declared their "no" to be a referendum in his favour. Someone tell me why I was ousted.
The child, identified as Ahmad, was among a crowd of supporters gathered to greet Nawaz Sharif as his motorcade passed through Lalamusa.
"We have to make sure that the mandate of the people is respected in the future".