All embassies are on high security alert, although no person or group has claimed responsibility for the blasts.
The explosions happened around noon and inflicted severe hand wounds to a member of the Swiss Embassy. Doctors said the man, 53, may lose his hand.
A mail room employee at the Chilean Embassy was injured in a blast, but not seriously.
"We can't understand why we were attacked in this way," the Chilean ambassador said. "The package was addressed to the cultural office and was opened by the civil servant who injured himself as he opened it. His life is not in danger but there was blood everywhere."
The Ukrainian Embassy reported it earlier had investigated a suspicious package that was found to contain no dangerous device.
Italian Foreign Minister Franco Frattini said foreign embassies in Rome faced a "serious threat."
A spokesman at the British Embassy said they recently took extra precautions. "We have increased security with regard to the screening of incoming mail, but we have not had any incidents here. We have advised all staff to let security know when parcels and letters arrive so that they can be thoroughly checked."
Earlier this week a bomb was found inside a shoebox on an empty train carriage on Rome's subway. Police said the homemade device, found under a seat by a transport worker at 10 a.m., had no detonator.
The subway bomb "could have been a warning action," Maurizio Mezzavilla, head of the Carabinieri paramilitary police force in Rome, said. "The device was well put together. It was done by an expert."
Police said the bombs may be part of an international anarchist group seeking publicity.
Rome Mayor Gianni Alemanno said city police are working with Interior and Foreign Ministry officials. "It's a wave of terrorism against the embassies. There is an international element to this," he said.
The Rome bombs are the latest in a spate of parcel bomb attacks on leading Western European politicians in major cities, in particular Athens, since October.
Interior Minister Roberto Maroni said investigators are considering possible connections with anarchists "following analogous incidents" in November in Greece. "These are very violent groups present also in Spain and Greece with close links between them," Maroni said.
A woman courier at a private delivery company in an Athens suburb was injured when a package addressed to the Mexican Embassy exploded in her hands.
Police later arrested two suspects, one wearing a bulletproof vest and carrying a handgun.
Also in Athens, mail bombs exploded outside the Swiss and Russian embassies.
In Berlin, a suspicious package was found in the mail room of the office of German Chancellor Angela Merkel.
Police in France arrested two men on suspicion of trying to post four parcel bombs to President Nicolas Sarkozy and the Mexican, Dutch and Belgian embassies. Police said the men were disguised, wearing body armor and carrying handguns.