Initially, one fan wearing a white T-shirt went out to give Acuña a hug before he was pulled off of him by multiple security guards.
As that was happening, another fan, also wearing a white T-shirt, approached Acuña and greeted him, and then pushed Acuña over, before the fan was taken down by security.
Eventually, the two fans were escorted off the field by security.
[DOWNLOAD: Free WSB-TV News app for alerts as news breaks]
It is unclear if the men knew each other prior to running onto the field.
The 25-year-old Acuña had one of his best games at the plate on Monday, going 4-5 and hitting his 29th home run of the season.
The Braves won the game 14-4 and improved their MLB-best 85-45 record.
[SIGN UP: WSB-TV Daily Headlines Newsletter]