The group included a longtime member of the grounds crew, ticket office employees, warehouse employees and a member of the maintenance crew, and even a couple season-ticket holders.
Rivera has met with longtime employees at each city he's visited during his final season in the Major Leagues. He's retiring following Sunday's game.
"It was really special, really to the point it was almost surreal," said Astros director of box office operations Bill Cannon. "The man is truly larger than life. I say that unabashedly, yet a man of very genuine humility and compassion. He's at the top of his team, literally a legend.
"A lot of us [work] laboriously and don't have contact with the players. We don't bemoan that. People on the outside say, 'Don't you play dominoes with them on the off-day,' so for him to take time to meet with the rank and file was special."
Rivera met with about 25 people Saturday and took time to answer questions, pose for pictures and give each one an autographed ball.
Cannon, 68, has been with the Astros since 1977.
"By virtue of just having lived a while, you can see what's real and what's fake," he said. "With him, it's real as it gets."