Iraqi interior ministry sources said armed men in three cars blocked a road in the upmarket Mansour district on Saturday and opened fire on the embassy vehicle. A police source and a nearby resident said the victims had been buying food.
The men opened fire on the vehicle, killing one person before kidnapping the rest, reports said.
Reuters Television footage showed a white 4WD vehicle with a smashed window in front of a grocery store, its trunk filled with vegetables and other foodstuffs.
Blood on the pavement suggested someone had been shot outside the car, but this could not immediately be confirmed.
Later in the day, a suicide car bomb exploded in the southern port city of Basra, killing 21 people and wounding 80, police said. It came three days after Nouri al-Maliki, the prime minister, announced a security crackdown there.
Police sources said the bomb exploded in a crowded bazaar in the old part of the city, where al-Maliki launched a one-month state of emergency on Wednesday to tackle criminal gangs and Shia factions whose feuding threatens crucial oil exports.
Stores in the historic area, which sell mostly mobile phones, were badly damaged, windows smashed. Pools of blood could be seen in the streets.
The head of Russia's foreign ministry's information department, Alexei Sazonov, told NTV television that "according to information from Baghdad, four Russian diplomats from the Russian embassy were kidnapped while on duty and another was killed by unidentified men".
Russia's foreign ministry said it has set up a crisis cell to find and free the four Russian embassy employees.
"Having been informed about the kidnapping of four Russian embassy employees in Baghdad, the foreign ministry has not delayed in creating a crisis cell to co-ordinate actions to bring about the liberation of these Russian citizens as rapidly as possible," a statement said.
The ministry's statement said the attack happened at 1:45pm Moscow time (1145 GMT), while Sazonov put it at 10 minutes earlier.
It was still unclear if those kidnapped included diplomats. "We are trying to clarify the situation on the spot," a spokesman for the Russian foreign ministry said earlier.
But he added: "They are all Russians, there are no Iraqis among them."
The Iraqi interior ministry said it had alerted police to be on the lookout for a car and minibus carrying the hostages.
Hundreds of foreigners, including diplomatic staff from several nations, have been kidnapped and dozens killed since the US-led invasion of Iraq in 2003.