It was not immediately known who planted the bomb.
Police at the scene said seven people were killed in the blast.
Officials said the car exploded outside a bank in a shopping center near the U.S. Embassy, which is a heavily secured fortress-style building in an upscale district of the capital.
Radio reports said several buildings were badly damaged and three cars were on fire.
Bush, who leaves Washington Thursday for a U.N. development conference in Monterrey, Mexico, was due to arrive in Lima Saturday for his first visit to South America.
U.S. officials were not immediately available to comment on the attack.
Peru was rocked by leftist rebel violence by the Shining Path and Tupac Amaru Revolutionary Movement, or MRTA, guerrilla groups in the 1980s and 1990s whose wars on the state cost 30,000 lives.
Peruvian authorities said late last year it had foiled a Shining Path attack on the embassy and other U.S. missions.