Police said all the wounded were in critical condition.
Zadran, the leader of an ethnic Pashtun tribe and a former anti-Soviet fighter, is an MP for Paktia province in southeast Afghanistan.
He has often criticised the Taliban and has accused neighbouring Pakistan of aiding them.
Speaking to James Bays,
Al Jazeera's correspondent, in Kabul shortly after the attempt on his life, Zadran was blunt. "These people are the enemies of Afghanistan and the world," he said.
"We call them al-Qaeda. Pakistan and ISI, its intelligence agency, trained them there and sent them here."
Bays reported quoting an Afghan police officer that security for Zadran had been tightened recently based on increased threat perception.
The Taliban have waged a tough and effective anti-government campaign across Afghanistan this year. Nearly 4,000 lives have been claimed in violence this year.
In mid-December, police said they arrested an Afghan national named Rasoul Khan Sartak on charges of planning to assassinate Zadran. Sartak is currently in police custody.
"Rasoul Khan Sartak has confessed he was sent on a mission to assassinate Padshah Khan Zadran and we have convincing documents. He is in our custody now," said Ali Shah Paktiawal, a police criminal investigation chief.
Taliban fighters have launched several other attacks in the past against politicians opposed to the movement.
Hakim Taniwal, governer of Paktia province, was assassinated in a suicide bombing in September, becoming the first governor to be killed since the Taliban were toppled.
On December 12 a suicide bomber blew himself up at a governor's house in southern Helmand province, killing eight people. Mohammad Daud, the governor, survived the attack.
Police in southern Afghanistan said Tuesday they arrested a would-be suicide bomber with explosives strapped to his body who planned to kill the governor of Ghazni province.
Hamid Karzai, Afghan president, and other officials have openly blamed Pakistan's government for supporting the Taliban and giving them safe haven in Pakistan, training and financial support.
Islamabad strenuously denies such accusations.