Interior ministry spokesman Ivan Netik said the country was due to take 200 people from camps in Turkey, Italy and Greece under an EU relocation scheme to spread out the number of refugees across Europe.
But he said his nation would rather the people were Christian because "we don't have any mosques in Slovakia".
Mr Netik told the BBC: "We want to really help Europe with this migration wave but... we are only a transit country and the people don't want to stay in Slovakia.
"We could take 800 Muslims but we don't have any mosques in Slovakia so how can Muslims be integrated if they are not going to like it here?"
Countries have been urged to take an "inclusive approach" to relocation by the UN's refugee agency.
Mr Netik denied he was discriminating against Muslims and said they would not be able to integrate properly.
He added that community cohesion was his priority.
EU Commission spokeswoman Annika Breithard told the BBC she would not comment on the Slovakian statement but added that states were banned from any form of discrimination.
