Indian police said a bomb hit an embassy car and wounded a woman. She was not immediately identified and there was no word on her condition.
There was one attempted attack, and one successful, as it were, said Paul Hirschson, a spokesperson for Israel's foreign ministry.
In both cases, the people concerned worked with the Israeli embassies. He also confirmed that a bomb had been found in a car belonging to a staffer at the embassy in the Georgian capital Tbilisi, which was defused by local police.
Hirschson said the Israeli ambassador to India was not hurt in the New Delhi attack.
Israel had put its foreign missions on especially high alert ahead of the February 12 anniversary of the assassination, in 2008, of the military mastermind of Lebanon's Hezbollah guerrillas, linked to the Shi'ite Islamist group Hezbollah, Imad Moughniyeh.
Iranian-backed Hezbollah had vowed to avenge Moughniyeh's death in a Damascus car-bombing, blaming it on Israel.
Israelis had also warned of possible reprisals ordered by Tehran for the assassination of several scientists involved in Iran's controversial nuclear programme. No-one has claimed responsibility for the Iran killings.