The Hungarian law was approved almost unanimously, with 344 votes for, three against and five abstentions in a vote followed by long applause.
Almost simultaneously, Slovakia voted to amend its own citizenship law, stripping anyone of their Slovak citizenship if they apply for Hungarian nationality.
Southern Slovakia is home to roughly 500,000 ethnic Hungarians, about a tenth of the country's population of 5.4 million. Many ethnic Hungarians live in Slovakia and Romania, as a result of post-World War I division of the Austro-Hungarian empire.
Slovak leader Robert Fico has called Hungary's move a "security threat", BBC reported. He told the Slovak parliament on Tuesday that Hungary was attempting to revise history, and accused Hungary of gross ignorance of the bilateral friendship treaty.
The Slovak draft amendment also states that holding any public position in the Slovak Republic is bound to Slovak citizenship.
Aside from the Hungarian case, dual citizenship is generally allowed in Slovakia.
Slovakia's Hungarian Coalition Party (SMK) welcomed the adoption of the amended Citizenship Act by the Hungarian Parliament.
"The SMK considers the hysteria stemming from adoption of the bill from the side of the Slovak cabinet as inappropriate and exaggerated," the party wrote in a statement, as quoted by SITA agency.
But many Slovak politicians say they see the idea of dual citizenship for its large ethnic Hungarian minority as an attack on the small nation's sovereignty.
Slovakia will hold national elections on 12 June, which the centre-left SMER party led by Prime Minister Robert Fico is poised to win, but may find it difficult to form a majority coalition.
The latest opinion poll showed that he may even be squeezed out by a wide, five-party centre-right coalition of opposition factions.
The country, which joined the euro zone last year, needs to slash its budget deficit, axe a high jobless rate, boost law enforcement and improve the business environment. Corruption remains a burning issue, according to opposition parties.
The Christian Democrats (KDH) said they preferred a wide opposition coalition to any cooperation with Fico.
"KDH will not enter a post-election government relationship with SMER," Jan Figel, head of the Christian Democrats, told reporters.
"We will do all that is possible for the victory of a centre-right alternative," he added.