NFL spokesman Michael Signora confirmed that the play was reviewed by the senior football operations staff and there will be no action taken against Suh.
While there was contact between the players, Suh's action was not deemed a kick. Morris was on the ground after a tackle when the incident occurred.
"The league looked at it and they made their ruling. I watched the play. Ndamukong has been doing a great job since he's been here. He's been working extremely hard and he's a great teammate. I expect him to continue to do that and continue to play well," Dolphins coach Joe Philbin said Monday.
Redskins coach Jay Gruden said he respected the Dolphins' coaching staff and said the play in question was just part of the game.
"Coach Philbin, Coach Coyle on defense, those guys are good coaches. They don't teach anything dirty. Sometimes things happen in the course of a game that look like they're dirty, but it's part of the game," he said. "I have a lot of respect for that team and that staff, and they beat us. I'm not going to make any accusations."
Following the game, Suh claimed not to remember the incident.
"I tackled him plenty of times during the game, so I'm not really certain what you are speaking of," he told reporters.
Suh, who signed a six-year, $114 million contract with the Dolphins as a free agent in March, has a reputation as a "dirty" player following a history of being fined for player-safety violations. In all, Suh has lost $420,669 due to fines and suspensions in his career.
ESPN's Adam Schefter, James Walker and John Keim contributed to this report.