Russia said it was "wrong" to ratify the treaty to join the international court, which in March issued an arrest warrant for President Vladimir Putin over the war in Ukraine and the illegal deportation of children to Russia.
ICC members are expected to make the arrest if the Russian leader sets foot on their territory.
The vote illustrated a growing chasm between Moscow and Yerevan, which has grown angry with the Kremlin over its perceived inaction over Armenia's long-standing confrontation with Azerbaijan.
Azerbaijani forces last month swept through the breakaway region of Nagorno-Karabakh -- where Russian peacekeepers are deployed -- and secured the surrender of Armenian separatist forces that had controlled the mountainous region for decades.
An online broadcast from the Armenian parliamentary session showed a majority of 60 deputies voting in favour of the proposal, with 22 -- mainly opposition lawmakers -- voting against joining the ICC.
The Kremlin immediately criticised Armenia's decision.
"We are doubtful that, from the point of view of bilateral relations, Armenia's accession to the Rome Statute is correct," Kremlin spokesman Dmitry Peskov told reporters.
"We still believe that it is the wrong decision," he added.
'Nothing better'
Tensions have also been rising between Yerevan and Moscow over the role of Russian peacekeepers in the self-proclaimed republic of Nagorno-Karabakh, which announced its dissolution last week following the lightning military operation by Baku.
The territory lies within the internationally recognised border of Azerbaijan.
Armenian's Prime Minister Nikol Pashinyan last week sought to assuage Kremlin fears, saying the initiative was not "directed against" Russia.
"It comes from the interests of the country's external security, and taking such a decision is our sovereign right," he said.
Pashinyan has been critical of Moscow's refusal to intervene during Azerbaijan's offensive, and previously said his country's foreign security alliance with Moscow was "ineffective".
The Kremlin struck back again on Tuesday.
"The Armenian side has nothing better than these mechanisms," spokesman Dmitry Peskov said.
On Tuesday, Armenia's representative on international legal matters, told parliament that the decision was focused on the country's security concerns.
"We are creating additional guarantees for Armenia" in the face of the threat to the country's territorial integrity from arch-foe Azerbaijan, said Eghishe Kirakosyan.
It was an apparent reference to May 2021, when Azerbaijani forces occupied a small pocket of land inside Armenia, near the countries' shared border.
The arch foes have been locked in a decades-long rivalry.
Kirakosyan said that Yerevan had proposed signing a bilateral agreement with Moscow to alleviate Russia's concerns over the ratification of the Rome Statute.
Dissolution
Armenia signed the Rome Statute in 1999, but did not ratify it, citing contradictions with the country's constitution.
The constitutional court said in March those obstacles had been removed after Armenia's adoption of a new constitution in 2015.
After the offensive in September, most of the Armenian population fled the self-proclaimed republic of Karabakh, whose authorities announced that it would be dissolved by January 1, 2024.
After the fall of the Russian Empire, the mountainous region, populated mainly by Armenians who regard it as part of their ancestral land, has been part of Azerbaijan.
It unilaterally proclaimed its independence with the support of Armenia when the Soviet Union collapsed in 1991.
Karabakh separatists resisted Baku with the support of Yerevan for three decades, notably during the first Karabakh war from 1988 to 1994 and the second in 2020.
That six-week war ended in a deal brokered by Russia that saw the 2,000-strong peacekeeping contingent deployed.
The international community never recognised the territory's independence.
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