The confirmation came after investigative news website Insajderi.com reported Saturday that Ragip Mustafa had requested asylum in Germany's southwestern Rheinland-Pfalz state.
According to a document published by the news portal, he applied for asylum on June 24, only days before his brother was received by German Chancellor Angela Merkel in Berlin.
"It's true. I was informed after it occurred ... that he had requested asylum outside the country, in order to seek medical assistance for a difficult disease which could not be cured in Kosovo," Mustafa wrote on his Facebook page.
Kosovo is one of the poorest countries in Europe, and the only one from the Balkans not to enjoy the EU's Schengen visa-free travel regime.
More than a million refugees and migrants swept up through the Balkans in 2015 heading for Europe, most of them from Syria, Iraq and Afghanistan.
According to EU statistic office Eurostat, around 70,000 Kosovars applied for asylum in the last two years, making it the fourth largest asylum-seeking nation after Syria, Afghanistan and Iraq.
Mustafa said his brother was not the only family member to leave for Germany: his nephews and nieces had taken the same illegal migrant route via Hungary, and were returned afterwards.
"This only proves that my family shares the fate of the rest of the citizens of Kosovo, the problems they face," Mustafa wrote on Facebook.
"As prime minister I am trying to find a solution, to ensure visa liberalisation, to attract investment and to create job opportunities, to improve the health system, so that fewer of our citizens need to request
healing outside the country," he added.
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According to Insajderi.com, the premier's brother took the same illegal route as thousands of other Kosovars, through the Serbian-Hungarian border, making his way initially to France, where his first asylum request was denied.
Ragip Mustafa then went to Germany, where he applied for asylum again, the report said.
Kosovo, a former Serbian breakaway province put under UN administration after the 1998-1999 war,declared independence in 2008.