Two young women also died when a Taliban fighter drove his explosives-laden car into a foreign convoy near Kabul's international airport, the latest attack of Afghanistan's fighting season.
Mr Hammond described the attack, which the Taliban has claimed responsibility for, as "cowardly".
"This is the second attack in a matter of days for which the Taliban have claimed responsibility and I strongly condemn their cowardly actions," said Mr Hammond.
"I can confirm that a British security contractor is among those killed in the attack." His family has been informed and my thoughts are with them at this incredibly difficult time. Consular staff stand ready to provide support.
"Two Afghan women have also sadly lost their lives and many more have been injured. These attacks must not stop the people of Afghanistan, with the support of the international community, working towards a more peaceful future."
A Foreign Office spokesman added: "We can confirm that a British national was tragically killed in a terrorist attack in Kabul this morning."
"We stand ready to provide consular assistance to the family."
"All mission members who were in the vehicle are in a safe place and their injuries are not believed to be fatal," said EUPOL spokesman Sari Haukka-Konu. "A non-EUPOL person inside the vehicle is deceased."
"A suicide bomber detonated his Toyota sedan targeting a foreign forces convoy near Kabul airport today at 9am," said Kabul police spokesman Ebadullah Karimi.
The Taliban have waged a 13-year war to topple the US-backed government in Afghanistan, and official efforts to bring the insurgents to the negotiating table have so far borne little fruit.
The surge in attacks has taken a heavy toll on Afghan civilians, according to the United Nations Assistance Mission in Afghanistan (UNAMA).
In the first four months of 2015, civilian casualties from growing attacks jumped 16 percent over the same period last year, a recent UNAMA statement said.