Ley was reporting from Havana, Cuba shortly after an exhibition game between the Tampa Bay Rays and the Cuban national team ended.
The demonstrator could be seen throwing flyers up in the air.
He was soon taken into custody by police.
Ley later tweeted one of the flyers, adding, "Everyone ok down here."
Front of the pamphlet thrown by protesters at out Havana live shot. Everyone ok down here. pic.twitter.com/1qVfPvT82V— Bob Ley (@BobLeyESPN) March 22, 2016
The Rays won the game 4-1 in the first visit by a major league team to the communist island since 1999.
Both presidents Barack Obama and Raul Castro were in attendance.
ESPN contributed to this report.