The bill would have required a religion to have at least 50,000 followers to become official and qualify for state subsidies
"This law infringes fundamental rights," Kiska said in a statement, a couple of weeks after Slovak lawmakers adopted the legislation tabled by the right-wing Slovak National Party (SNS), a governing coalition member.
The bill would have required a religion to have at least 50,000 followers to become official and qualify for state subsidies, up from the current 20,000.
Only between 2,000 and 5,000 Muslims live in the country of 5.4 million people.
Governing coalition lawmakers are expected to override the veto, in accordance with the anti-Muslim rhetoric of leftist Prime Minister Robert Fico.
"While I am prime minister, I will never agree to establish a unified Muslim community in Slovakia," he told reporters on Tuesday.
Slovakia has 18 registered religious communities on which it spent nearly 40 million euros ($42 million) last year, according to the culture ministry.
The largest is the Roman Catholic church, with 3.3 million faithful.
By registering, religious communities can receive subsidies to notably help operate their schools and pay church salaries.
According Mohamad Hasna, president of the country's Islamic foundation, the fact that Muslims cannot register as a religious community significantly affects their everyday life.
"Muslims can't set up their own religious schools," he told AFP, adding that Islamic traditional weddings and funerals are also not legally binding in the country.