Yemeni media identified the diplomat as Katsusuke Sotomini, as did an official at the embassy in Sanaa who spoke on condition of anonymity due to regulations. An Associated Press journalist some 200 meters (220 yards) away from the embassy found blood stains where the attack apparently took place.
Dr. Atiq al-Maori of the Saudi-Germany Hospital in Sanaa said the diplomat suffered "multiple injuries" to his forearm and shoulder in the attack.
"We will keep him for observation to continue the treatment," the doctor said. "His medical situation is stable."
Abductions are frequent in Yemen, an impoverished nation where armed tribesmen and al-Qaida-linked militants take hostages to swap for prisoners or cash. Yemen is engaged in a rocky political transition since longtime autocrat Ali Abdullah Saleh stepped down in 2012 following mass popular protests.
The country's political turmoil has created a security vacuum, which al-Qaida in the Arabian Peninsula has used to seize large swaths of territory across the restive south. The U.S. regularly carries out drone strikes in the country targeting who it says are militants belonging to the group.
On Dec. 5, al-Qaida militants stormed the Defense Ministry in Sanaa, killing 52 people, including at least seven foreigners.
Separately, the country's parliament blamed the US for a recent airstrike in the central city of Radda that killed at least 15 people and asked the government to end the use of Yemeni airspace by US drones to pursue al-Qaida operatives.
The government acknowledged the death of civilians in the attack, saying an al-Qaida van had hidden itself in a convoy of civilian cars, later paying compensation to the families of victims. It did not however say whether government aircraft or US drones were behind Thursday's attack.
While the U.S. acknowledges its drone program in Yemen, it does not usually talk about individual strikes. Washington considers the local branch of al-Qaida the most active in the world, and had increased targeting of its operatives in Yemen.
The parliament, in its statement aired on state TV, said US drones in Yemen are a "blatant violation" of national sovereignty.
In a statement Friday, Amnesty International called on "whoever was responsible" for the attack "to own up to the error."
"The appalling lack of transparency over civilian deaths in Yemen means that when violations occur, the victims and their families have no effective access to redress or reparations. The utter lack of accountability for these killings must end," the group said.
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Associated Press writer Mari Yamaguchi in Tokyo contributed to this report.