Media reports said it was an apparent strike by the Shining Path guerrilla insurgency.
Cable news station Canal N broadcast images of police cordoning off the site of the blast, which shattered windows and blew a hole in the shutters of a closed storefront. The explosion occurred on the same block as the National Election Board building.
Canal N reported that the woman and her 6-month-old daughter were at a nearby hospital, where they were being treated for minor injuries.
In the backpack that carried the bomb, police recovered pamphlets bearing the symbol of a red hammer and sickle and proclaiming "Long live the popular revolution" and "Long live President Gonzalo," Canal N and CPN radio reported.
President Gonzalo was the nom de guerre of Shining Path founder Abimael Guzman, who was arrested in 1992 and is serving a life sentence without parole in a maximum security naval prison.
The once-feared movement suffered a severe blow in July 1999 when its national leader, Oscar Ramirez Durand, was captured. Attacks by the group are infrequent. Ramirez Durand is now serving a life sentence at the same prison as Guzman.
Guzman recently went on hunger strike, demanding a re-trial in civilian court, but reportedly ended the campaign after authorities agreed to provide more lenient prison conditions.
Some 30,000 people have died since 1980s as a result of rebel violence, most of them civilians caught in the crossfire between guerrillas and security forces.
According to the Terrorism Research Center, Shining Path "considered by many to be the most dangerous and violent terrorist organization in the world" began its campaign in 1980 and has killed 10,000 to 12,000 people.
"The goal of this organization is the destruction of the existing Peruvian government in favor of an Indian-run socialist system," the research center says in a profile.
© MMI Viacom Internet Services Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report