"We represent the Pope in Syria and we won't leave the country," Archbishop Zenari told Adnkronos International (AKI) in a phone interview.
"If there are further attacks like today's we will move to another area," Zenari said, adding that the embassy was located in a "sensitive area" of the capital.
He was speaking after a rocket landed on a balcony at the Vatican embassy in central Damascus at 6.30 am, causing slight damage to the building but no casualties.
"I was just getting up when the rocket landed. I heard a very loud explosion and threw myself onto the floor, well away from the window, as a first rocket is often followed by others," Zenari told AKI.
Rubble and shards of glass fell into the garden from the third-floor balcony where the rocket landed, but embassy staff had not yet arrived for work, Zenari said.
"If the attack had happened just two hours later, people could have been hurt," he told AKI.
"At around 7 am, I usually pray at the window sill of my room, which is only a couple of metres from the balcony that was hit by the rocket," he said.
Around 10 rockets had landed within 150-200 metres of the embassy since March, but Tuesday's was the first to hit the building, Zenari said.
Ballistic experts from the Syrian military police visited the embassy after the strike to investigate, he said but declined to speculate on the rocket's provenance.
"I am very cautious. I can only say what happened but can't say if it was a targeted strike that was part of a precise strategy or an error," said Zenari.
Syria's deputy foreign minister Faysal al-Mukdad visited the embassy immediately after the attack "to express his solidarity and that of president Bashar al-Assad," Zenari said.