Smith, 53, posted a video of his oldest child catching a large spider under a glass bowl with the remark, "Posting this from a Holiday Inn," sounding horrified as he did so.
"Wow, what the h—l. Before his son convinced him that it was a tarantula, Smith said, "That is a big a— spider."
After a break from social media, the Academy Award-winning actor has only lately returned to the platform.
"I'm on a chair," Smith said in the video. "Alright Trey, you gotta get that out of here. Come on."
Smith added: "You're young and strong. You can handle the bite."
Trey was startled as he turned to face the camera, but he acted bravely and grabbed the eight-legged critter from beneath a glass bowl.
The spider was then moved outside after Smith unsuccessfully attempted to place a piece of paper underneath.