The intra-court appeal was filed by Riaz Hanif Rahi, a member of the Punjab Bar Council.
Musharraf's lawyer in the treason case, Mohammad Ali Saif, described Rahi as a "rogue lawyer".
"This petition has nothing to do with us. He is a rogue lawyer who has done it on his own. We are still in the process of devising our strategy. He had filed such petitions earlier that were rejected," Saif told PTI.
In the petition, Rahi said the special court violated the Constitution and the law. He named the Law Ministry, the Interior Ministry, the special court's registrar and Federal Investigation Agency chief as parties in the case.
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This is the first time in Pakistan's history that a former general or dictator is facing trial. If convicted of treason, Musharraf could face either life imprisonment or the death penalty.
Musharraf came to power in 1999 by toppling a government led by current Prime Minister Nawaz Sharif and ruled till 2008, when he was forced to resign after being threatened with impeachment.
He lived in self-exile for about five years and returned to Pakistan in March but was hauled to court in different cases, including one over the 2007 assassination of former premier Benazir Bhutto.