Raila Odinga, the prime minister, confirmed the death toll.
"It is a very, very regrettable incident, and this incident is condemned in the strongest terms possible.
"I want to say clearly that the government will do everything possible to get to the root of this incident. We must condemn this," Odinga said at the site of the blast.
"Kenyans can decide peacefully what they want" concerning the constitution, he said.
Witnesses said the first blast took place at the back of the crowd, and that a speaker on the podium told the crowd to move toward the front, fearing an electrical blast.
But minutes later a second blast took place toward the front of the crowd, wounding dozens more people.
Steve Odhiambo, a 28-year-old mechanical engineer, said rally participants were taking part in a prayer when the first explosion occurred. Darkness was setting in and the rally was just about to finish.
"I was about 50 metres from the blast, and I saw one person who had his lower body blasted off," Odhiambo said while wearing surgical gloves after helping take a woman to a hospital. The woman died of her wounds.
The campaign against the draft constitution opposes a clause that would allow abortion to save a mother's life. Opponents also do not like a clause that would recognize informal courts used by Kenya's Muslim community.
A prominent backer of the campaign against the draft, William Ruto, the agriculture minister, called the attack "the darkest hour of our nation".
"Innocent blood has been shed by people with evil desires, and we are calling upon the police to take action," he said.
"The decision of whether we are going to have a new constitution or not belongs to the people of Kenya, and they have the right to say this or not. Those of us who are saying 'no' have committed no crime."