The New Yorker reported the meeting earlier this week and it has now been confirmed by the White House.
The development comes amid pressure for Attorney General Jeff Sessions to resign over his two conversations with Mr Kislyak during Mr Trump’s election campaign.
Six of Mr Trump’s team – including Paul Manafort, Carter Page and Michael Cohen – have allegedly had undisclosed contact with Russia officials.
“They generally discussed the relationship and it made sense to establish a line of communication,” said White House director of strategic communications Hope Hicks, as reported by the New York Times.
“Jared has had meetings with many other foreign countries and representatives — as many as two dozen other foreign countries’ leaders and representatives.”
The meeting lasted 20 minutes and that Mr Kushner has not met with Mr Kislyak since, said Ms Hicks.
The brief encounter was held at a time when the US was expelling 35 people suspected of being Russian spies.
When first asked in January, the White House said Mr Flynn only shared a text message and phone call with the Kremlin diplomat.
Mr Flynn resigned, making him the shortest holder of White House office ever, after giving Vice President Mike Pence "incomplete information". Mr Flynn allegedly reassured Mr Kislyak that Russia would be given softer treatment following Mr Trump's inauguration.
Mr Kislyak, an engineering graduate and previous ambassador to Belgium, is considered to be a spy by US intelligence officials.
The Independent has contacted Ms Hicks for further comment.