Molinari and his brother Francesco both played in the 2010 edition when Europe regained the trophy in Wales.
"It is fantastic. I played the Ryder Cup in 2010 and to be able to be a vice-captain in this one is a dream come true," Molinari said in a statement.
"It was a very unexpected call from Henrik. We had chatted a few times about stats and what I could do to help the team, but I never expected this.
"The Italian fans will be loud and passionate at Marco Simone. For the players, it will be a lot of fun to play in front of such supportive crowds."
Stenson had named Denmark's Thomas Bjorn -- who captained the team to victory in the 2018 edition -- as his first vice-captain earlier this month.