There was no immediate claim of responsibility for the attack on Nabil Amr, who was hit twice in the right leg by bullets fired into his home in the West Bank city of Ram Allah.
Doctors said his injuries did not appear to be life-threatening.
Palestinian police said they had opened an investigation into the night-time shooting, carried out against the backdrop of a leadership crisis in the Palestinian Authority (PA) over demands for democratic reforms.
Arafat is facing the stiffest test of his leadership since Palestinians obtained limited self-rule from Israel in Gaza and the West Bank a decade ago. Some fear the strife could eventually escalate into civil war.
"We were sitting inside when someone shot at him from the window," Amr's son, Marwan, said.
Palestinian sources said Amr, a former information minister, has long been at odds with veteran leader Arafat over the pace of reform in institutions seen by some as out of touch.
Amr, 47, was shot minutes after returning home from a television interview in which he criticised Arafat's performance as president. His residence has been shot at in the past.
Chaos in Gaza
Prime Minister Ahmad Quraya submitted his resignation to Arafat on Saturday, complaining about chaos in Gaza, where Palestinians demanding anti-corruption moves have fought security forces.
Quraya, who has said he would remain in office for now after Arafat rejected his resignation, is frustrated over Arafat's refusal to allow him to reform Palestinian institutions and a jumble of security services ridden by cronyism.
Seizing on the unprecedented challenge to Arafat's leadership, the United States revived its demand he give up powers to end turmoil in the Gaza Strip.
"It is chaotic at the moment," Secretary of State Colin Powell said.
"We believe the correct path forward involves Mr Arafat yielding power, real executive power to a prime minister, for that prime minister to do what is needed for the Palestinian community.
"And when that happens, then we can get moving on a road map. We can deal with not only the security problems, but the economic problems that are afflicting the Palestinian people," he added.
Arafat shuffled his security chiefs on Monday after the demonstrations.
The unrest is indicative of a power struggle that has erupted between Arafat's old guard and a younger, pro-reform generation in Fatah possibly staking out turf before Israel implements a plan to evacuate Jewish settlers from the Gaza Strip in 2005.