He is the second Taoiseach to suffer a mishap at the Irish Management Institute (IMI) in south Dublin.
Several years ago, former Taoiseach Brian Cowen had a poster fall on him while he was attending an event there.
Mr Kenny and Mr Schmidt were posing for photographs at the IMI, where they were giving speeches to business leaders.
Mr Kenny, a former Gaelic footballer, kicked the rugby ball he had been given into the air and caught it.
That prompted Mr Schmidt to attempt his own Gaelic football-style solo while Mr Kenny was standing beside him. But when he kicked the ball, he hit Mr Kenny in the face.
Mr Kenny was stunned for a second, but quickly recovered and joked to the photographers present: “Did you get that?”
Mr Schmidt quickly apologised.
And during his speech to business people afterwards, Mr Schmidt said he had lost control of the ball. But he praised Mr Kenny’s reaction, saying that “he took it well”.
Last week, Mr Kenny said he’d got a “wallop” after voters rejected his plan to abolish the Seanad. He referred to this in his speech, saying there was a need to “roll up the sleeves and lead by example”.</>\[D.hardiman\]”Sometimes you don’t win them all but you have to have a vision of where you want to be,” he said.
By Michael Brennan