The serial explosions occurred around 5:30 p.m. in the old town of the Shiite holy city, some 180 km south of Iraqi capital Baghdad, the official told Xinhua. Some shops and buildings were also damaged.
One was a car bomb near a mosque. The other two were roadside bombs near a popular market, according to the source.
Najaf is home to the mausoleum of Imam Ali, the cousin of the Prophet Mohammed. It attracts tens of thousands of pilgrims every year.
Iraqi officials have warned that violence is expected to rise ahead of the country's March 7 parliamentary election. On Tuesday, security forces arrested 25 terrorist suspects and more than 400 kg of explosives in a sweeping operation in Baghdad.