Vatican.va was attacked on Monday evening, the website The Hill reported.
The hacker, calling himself THTHerakles, claimed credit for the attack on Twitter.
Pope Francis sparked fury from Turkey on Sunday after he used the word "genocide" to describe the killings of Armenians at the hands of the Ottoman empire.
Turkey then summoned the Vatican's ambassador in Ankara and recalled the Turkish envoy to the Holy See in a show of protest.
The European Parliament is due to vote on Wednesday on a "motion for resolution on the commemoration of the centennial of the Armenian genocide".
Turkish President Recep Tayyip Erdogan warned Turkey would ignore any decision by the parliament qualifying the 1915 killings of Armenians in World War I as genocide, saying such recognition would go "in one ear and out from the other".
The vote takes place against the backdrop of growing tensions over the characterization of the tragedy ahead of the 100th anniversary of the massacres this month.
"Whatever decision the European Union Parliament makes today would go in one ear and out from the other because it is not possible for Turkey to accept such a sin or crime," Erdogan told reporters at Ankara airport before leaving for Kazakhstan on Wednesday.
The US on Tuesday called for a "full, frank" acknowledgement of the mass killings while shying away from calling it a "genocide."
"I don't know right now what sort of decision they will make...but I barely understand why we, as the nation, as well as print and visual media, stand in defence," Erdogan said.
"I personally don't bother about a defence because we don't carry a stain or a shadow like genocide," he said.
Armenia and Armenians in the diaspora say 1.5 million of their forefathers were killed by Ottoman forces in a targeted campaign to eradicate the Armenian people from Anatolia in what is now eastern Turkey.
Turkey takes a sharply different view, saying hundreds of thousands of both Turks and Armenians lost their lives as Ottoman forces battled the Russian Empire for control of eastern Anatolia during World War I.
Erdogan said Turkey was home to some 100,000 Armenian citizens, who were working in the country, some illegally.
"We could have deported them but we did not. We're still hosting them in our country. It is not possible to understand such a stance against a country which displays hospitality."
Turkey is also still home to a small Turkish-Armenian community, mostly based in Istanbul, who number around 60,000.
Armenians around the world will commemorate the 100th anniversary of the tragedy on April 24th, the same day as Turkey is planning major commemorations of the World War I battle of Gallipoli.