This answer varies for countries. Some yes, and some no.
He was born in Scotland, but served as Britain's Prime Minister.
Tadeusz Tomaszewski - Prime Minister - was born in 1881.
Henny Eman - prime minister - was born in 1944.
Mohammad Yusuf - prime minister - was born in 1917.
Prime Minister Manmohan Singh was born on September 26, 1932.
Abdul Zahir - Afghan Prime Minister - was born in 1910.
The second prime minister of Australia, Alfred Deakin, was born on the 3rd of August in 1856.
Yitzhak Rabin.
There are at least three Prime Ministers who have been born on 11 January.John A. Macdonald, first Prime Minister of Canada,was born on 11 January 1815.Jean Chrétien, twentieth Prime Minister of Canada, was born on 11 January 1934.Zenko Suzuki, Prime Minister of Japan, was born on 11 January 1911.
Orette Bruce Golding, Prime Minister of Jamaica, was born 5 December 1947.
Hans Georg Jacob Stang - prime minister - was born in 1830.
Joseph Lyons was born in Stanley. He has been Australia's only Tasmanian-born Prime Minister to date.