The building in Cairo near Tahrir Square was torched in the 2011 uprising that toppled Mubarak.
Demolition workers also began tearing down a nearby office block that was once the centre of state bureaucracy.
Egypt's government approved the move in April and said that the land would be given to the neighbouring Egyptian Museum.
Mubarak's National Democratic Party (NDP) was dissolved in April 2011 and its assets, including its headquarters on the River Nile, were seized.
BBC Middle East editor Alan Johnston says that those who rose up against Mubarak will certainly welcome the demolition work.
But he says that many will be deeply disappointed that in other, more important ways, their revolution failed to fulfil their expectations.
Mubarak was sentenced to three years in jail on corruption charges after a retrial earlier this month.
His original conviction was overturned in January over legal procedures.
The ex-leader remains in the Maadi Military Hospital in Cairo where he has been held amid his trials.
His two sons were also given four years in prison in the same case, which centres on the embezzlement of $14m (Â£9.2m) earmarked for renovation of presidential palaces.
In June, Egypt's highest court is due to decide whether to allow an appeal against a lower court ruling that dropped murder charges against Mubarak.
Egypt has begun demolishing the headquarters of the now-dissolved party of former President Hosni Mubarak.