Some mourners chanted "Death to Musharraf" - directing their anger at General Pervez Musharraf, the Pakistani president. Others chanted "Death to America".
Some threw stones at enclosures in the stadium holding senior government officials, shattering windows. No injuries were reported.
Hundreds of police and paramilitary officers had been deployed around the stadium, a senior police official said.
Jan, a former member of parliament and head of a local college of religion, had been regarded as a friend of Mullah Omar, an Afghan Taliban leader.
He was in a group of Pakistani scholars who travelled to Afghanistan in late 2001 to convince Omar that he should expel Osama bin Laden from Afghanistan to avoid attacks by the US.
Omar rejected the idea and a US-led invasion launched later that year overthrew the Taliban government.
Jan's body was buried in the grounds of a school that he helped to set up on the outskirts of Peshawar.