Powerful blasts ripped through a truck close to a military base near Kandahar on Tuesday, just two days after the adoption by the interim government in Kabul of a new constitution.
Annan strongly condemned "heinous acts of violence" and sent his profound condolences to the bereaved families and the government of Afghanistan.
UN spokesman Fred Eckhard added "the secretary general was shocked and deeply disturbed".
In a report to the UN Security Council, Annan said the post-war peace process had reached a critical juncture and such violence could hamper elections planned for later in 2004.
"Afghanistan has experienced a deterioration in security at precisely the point when the peace process demands the opposite," he wrote.
Officials described the explosion as a "terrorist attack", although a spokesman for the ousted Taliban denied involvement.
Eckhard noted that the attack came one day after a grenade was thrown into the Kandahar compound of the UN High Commissioner for Refugees.
He said attacks on civilians in the past 90 days exceeded the number in the previous 20 months. The report was issued before Tuesday's Kandahar bombing.
Witnesses in the dry and dusty city saw pools of blood and shredded pieces of clothing and shoes strewn across the street after the explosion at about 08:00 GMT.
"At first there was a small explosion in which a child was injured," said local witness Gulalai. "When people gathered to help the child, the big explosion happened."
General Abd al-Wasi, spokesman for the corps commander of Kandahar province, also said the blast was a "terrorist act".
"The majority of victims were school children. This was a very bad incident."
Corps commander Khan Muhammad Khan said one man had been arrested on suspicion of coordinating the explosion. About 50 US and Afghan soldiers quickly sealed off the area.
Kandahar is the former bastion of the ousted Taliban, which has declared a war on foreign and Afghan soldiers and aid workers.