Per ESPN's Adam Schefter, Winston was fined $12,154 for the incident that led to Lattimore and Bucs wide receiver Mike Evans getting into a fight.
The incident occurred during the third quarter of the Saints' 30-10 victory over the Buccaneers. Winston, who was taken out of the game in the second half due to a shoulder injury, poked Lattimore in the back of the helmet after a play.
Lattimore responded by shoving Winston away. Evans flew in and knocked Lattimore to the ground, leading to a fight between the two teams. No one was ejected from the game, but Evans received a one-game suspension for his role in the altercation that will be served on Sunday against the New York Jets.
Winston issued an apology on Wednesday, telling reporters his "competitive nature" got the best of him in the heat of the moment.
Buccaneers head coach Dirk Koetter announced Monday that Winston was being shut down for "several weeks" to give his right shoulder time to heal.