Several other militants fled the scene in a stolen vehicle to a neighborhood where the U.S. Consulate in Jiddah is located, the Arab television station Al-Arabiya (search) reported. It said they took shelter in an uninhabited house about 700 yards from the consulate.
Police sealed off the area, and the consulate closed for the day.
Bank officials contacted by The Associated Press said that while the explosion was near the Jiddah branch of the Saudi-American bank, though not directly outside it.
Several bank officials, all speaking on condition of anonymity, said a "small explosion" took place in a car in the neighborhood at about 9 a.m., and nobody in the bank was hurt. They said the blast had not affected the bank's operations. The officials said police took away the car.
In what appeared to be a report on the same explosion, the official Saudi Press Agency quoted an Interior Ministry statement saying an explosion took place inside a moving taxi in Jiddah, injuring the driver in the hand. The report gave no other details, and only said the driver had a criminal record of drug offenses.
The blast came on the third anniversary of the Sept. 11 attacks in the United States, which were carried out by 19 Arab militants, including 15 Saudis, and were blamed on Al Qaeda terror network, which is headed by Saudi-born Usama bin Laden.
The U.S. Embassy spokeswoman in the Saudi capital Riyadh, Carol Kalin, told the AP she was investigating the report but was unable to confirm if there had been an explosion.
Another embassy spokesperson, Robert Keith, said that even though there had been "no incident" at its Jiddah consulate, the mission was being closed to the public Saturday as a "precautionary measure." Saudi security officials were not immediately available for comment.
Al-Arabiya said in a further report that an attacker was wounded and taken to hospital where he was under guard.
Saudi Arabia has been hunting Al Qaeda-linked militants behind a series of bombings and shootings in the Gulf kingdom that have targeted the U.S.-allied Saudi regime, security authorities and foreign interests.