Sobotka`s spokesman Martin Ayrer told AFP the government was taking steps to stop the attacks on the account.
"We don`t know who might be behind the attack but looking at the messages it`s obvious that it`s some neo-Nazis," he added.
"If my Twitter account is attacked by neo-Nazis, I take it as evidence that I`m doing my job well. I wish a happy Christmas to all people of good will who reject spreading hatred, prefer humanity and support democracy," Sobotka himself said on Facebook.
The Czech Republic has rejected the EU`s system of quotas for distributing refugees across the bloc to try to tackle the massive influx of people fleeing conflict, persecution and poverty in the Middle East and Africa.
Sobotka has however shown a friendly face towards migrants, unlike rival President Milos Zeman, who said that jihadists used the migrant wave as a way to slip into the EU.
One of the messages on the prime minister`s Twitter account called for a "white revolution".
"Democratic elites are devastating Europe. There is no other option but to raise arms, build a guillotine and take the law into our hands," said another.
Few asylum seekers have chosen to stay in the Czech Republic so far, with a majority heading to wealthier Germany and other western EU states.
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