Belarus is in a political crisis following an Aug. 9 presidential election marred by vote-rigging allegations that led to mass demonstrations against Lukashenko, who has been in power since 1994.
Lukashenko says he won re-election fairly and is the victim of a smear campaign by the West.
"We are compelled to withdraw our troops from the streets, have half our army on guard and close our state border with the West, first of all with Lithuania and Poland," Lukashenko said in a speech at a women's forum in Minsk.
"To our greatest regret, we are compelled to strengthen our border with brotherly Ukraine."
Polish government spokesman Piotr Muller said in a text message that Poland did not have any confirmation that the border had really been closed.
Polish deputy foreign minister Pawel Jablonski told Reuters by text message: "We take this as another element of the propaganda campaign, a psychological game which aims to create a sense of an external threat."
The Polish foreign ministry told state run news agency PAP that the border was operating as normal.
Lithuanian border guard chief Rustamas Liubajevas said the border there was also operating as usual.
"We don't know what this (announcement) means. Will they close border to cargo, or people, or something else? ... We need to wait and see what the announcement means and how it is implemented," Lithuanian foreign affairs minister Linas Linkevicius said.
(Reporting by Gabrielle Tétrault-Farber in Moscow, Alan Charlish and Alicja Ptak in Warsaw, Andrius Sytas in Vilnius; writing by Tom Balmforth; editing by Grant McCool)