The Taliban have warned civilians they would be targeted if they try to vote and at least 10 percent of polling stations are expected to be shut due to security threats.
Most foreign observers left Afghanistan in the wake of a deadly attack on a hotel in Kabul last month.
A veteran Associated Press photographer was killed and a senior correspondent of the same news agency was wounded on Friday when a policeman opened fire on the two women in eastern Afghanistan as they reported on preparations for the poll.
The National Directorate of Security intelligence agency said it had arrested a man and seized a cache of rocket-propelled grenades, assault rifles and police uniforms from a house in Kabul hours before the election began.
In the city of Kandahar, cradle of the Taliban insurgency, the mood was tense. Vehicles were not allowed to move on the roads and checkpoints were set up at every intersection.
Hamida, a 20-year-old teacher working at a Kandahar polling station, said more than a dozen women turned up in the first two hours of voting and added that she expected more to come despite the threat of an attack by the Taliban.
She said: "We are trying not to think about it, but it's a bit of a concern."
The election is a landmark after 13 years of struggle to quell an insurgency that has claimed the lives of nearly 3,500 members of a U.S.-led coalition of troops. Afghan casualties have been far worse, with at least 16,000 civilians and thousands more soldiers killed in the violence.
