Thursday's bomb in the former Taliban stronghold killed five people, making it the deadliest bomb attack in the country since August.
Rice is in Kabul to meet with US-backed President Hamid Karzai, Foreign Minister Abdullah Abdullah, and top American diplomats and military officials later on Thursday.
During her visit, Rice is expected to discuss a number of issues with Afghan officials, including counter-terrorism, democracy in Afghanistan and waging a war on drugs
"We'll continue to talk with the Afghans about reconstruction, about building an economy there, because that can be self-sustainable ... about the problems that they continue to face, continuing in the war on terror, and of course on the counter-narcotics side as well," she had said in Washington before the trip this week.
Afghanistan is Rice's third stop on a six-nation Asian trip. She arrived on Thursday in the capital Kabul from Pakistan. She is due to return later on Thursday to Islamabad for further talks with Pakistan's leadership.
Rice also visited India, and will travel to Japan, South Korea and China during the trip.
The Bush administration sees Afghanistan as a foreign policy success after US forces ousted the Taliban and set the country on a path to its first democratic presidential elections which were held last year.