"During the third quarter, after a play had ended, you struck an unsuspecting opponent in the back, knocking him to the ground. Your conduct clearly did not reflect the high standards of sportsmanship expected of a professional," NFL vice president of football operations Jon Runyan wrote in a letter to Evans to inform him of the suspension.
Evans will appeal the suspension, a source told ESPN's Jenna Laine.
If the suspension stands, Evans will miss Sunday's game against the New York Jets and will be eligible to return to the Buccaneers' active roster on Nov. 13.
Evans was flagged 15 yards for running across the field and drilling Lattimore in the back, then pouncing on Lattimore when he hit the ground. A Saints player then tackled Evans to get him off Lattimore.
The dustup started when Buccaneers quarterback Jameis Winston -- who was not playing at the time -- pushed Lattimore in the back of his helmet while appearing to suggest that he go back to his own sideline. Lattimore turned around and shoved Winston in the chest. Then Evans flew in for the tackle.
Before the suspension was announced Monday, Buccaneers coach Dirk Koetter called Evans' and Winston's actions "totally unacceptable."
"Totally, totally unacceptable behavior, first by Jameis and then by Mike. Jameis cannot, under any circumstances, come off the sideline when he's not even playing in the game. And trash talking is trash talking, but to go out and tap another player, touch another player, whatever you want to call it at all on the field -- that's inexcusable," Koetter said.
"The Saints player responded and then Mike responded. That's not acceptable either. That's not having your teammates' back. That's just wrong."
Koetter did not see the play live but after watching the play on tape he said that Evans and possibly Winston should have been ejected.
"If I would have known what I know [now], Mike probably should have been ejected. And maybe Jameis should have been ejected," he said.
Evans leads the Buccaneers in receptions (40), targets (72) and receiving yards (532), and his four touchdown receptions are tied with Cameron Brate for the team lead this season.
Evans and Winston are both captains on offense, which is especially concerning for Koetter.
"It doesn't matter if it's team captains or the 45th or 46th man on the roster -- that's not professional," Koetter said. "That goes against everything you would want your team to stand for. Those guys know that."
Koetter addressed the team about their on-field behavior on Monday.
"I thought Mike said the right things after the game and I'm sure Jameis will take his responsibility next time he gets a chance."
ESPN Stats & Information contributed to this report.