Fifteen others were wounded in the attack on Le Jardin, an Afghan-owned eatery, which caused a piercingly loud explosion and left a building engulfed in flames.
The attack comes a day after Afghanistan announced four-way talks in Pakistan on January 11, aimed at jump-starting peace negotiations with the resurgent Taliban.
"We can confirm a suicide car bomb attack on Le Jardin," Fraidoon Obaidi, the head of Kabul's Criminal Investigation Department, told AFP.
"We are busy extinguishing the fire at the scene... two Afghans have been killed and 15 others wounded," he added.
The Italian-run Emergency Hospital in Kabul said on Twitter that the fatalities included a 12-year-old boy who was declared dead on arrival.
Security forces cordoned off the area and firefighters and ambulances were seen rushing to the restaurant, which sports a large garden festooned with rose bushes and is a popular hangout for foreigners and wealthy Afghans.
Taliban spokesman Zabihullah Mujahid on Twitter claimed several foreigners had been killed and wounded in the suicide attack.
Taliban insurgents routinely exaggerate the death toll in attacks on government and foreign targets.
Friday's bombing evoked memories of an audacious Taliban attack on another restaurant popular with expats, the Taverna du Liban, in January 2014, which left 21 people dead, including 13 foreigners.
Then, desperate customers tried to hide under tables as one attacker detonated his suicide vest at the fortified entrance to the eatery and two other militants stormed inside and opened fire.
Uncertainty Over Talks
The latest attack comes just days after Pakistan's powerful army chief General Raheel Sharif visited Kabul to try to prepare the ground for fresh peace talks with the resurgent Taliban.
Both sides agreed to hold a first round of dialogue between Afghanistan, Pakistan, US and China on January 11 to lay out a comprehensive roadmap for peace, officials in Kabul said.
Pakistan -- the Taliban's historic backers -- hosted a milestone first round of talks in July but the negotiations stalled when the insurgents belatedly confirmed the death of longtime leader Mullah Omar.
But despite the growing bonhomie with Islamabad, analysts caution that any substantive talks are still a long way off.
On Monday, just a day after Sharif's visit, a Taliban bomber detonated an explosives-packed vehicle near Kabul airport, killing one civilian in an attack targeting a NATO convoy.
Observers say the intensifying insurgency highlights a push by the Taliban to make more military gains to try to achieve greater concessions during talks.
Afghan forces are currently battling to push back Taliban insurgents who seized large swathes of the key opium-rich district of Sangin in the southern province of Helmand.
The offensive has prompted the first British deployment to the volatile province in 14 months.
The deployment, in addition to a recent arrival of US special forces in the region, comes a year after NATO forces formally ended their combat operations in the country.
The British and US intervention has fuelled the perception that foreign powers are increasingly being drawn back into the conflict as Afghan forces struggle to rein in the Taliban.