Anderson, 24, shoulder-barged Morton at the end of an over during the West Indies' victory in the second one-day international at Edgbaston on Wednesday.
Morton reacted angrily to the shove and words were exchanged, with umpire Brian Jerling have to step in.
There was further tension between the players when Anderson pointedly gestured towards Morton after his dismissal in a match West Indies won by 61 runs to level the series at 1-1.
Both men were called to see match referee Mike Procter after the match but while Anderson was fined, Morton was found not guilty of breaching the International Cricket Council (ICC) code of conduct.
The warring pair will have a chance to go head to head again in the third and final one-day match at Trent Bridge on Saturday.
Procter, explaining his decision, said Thursday in an ICC statement: "I have no problem with players being aggressive on the field because our game is all about passion and commitment.
"But, at the same time, they have to recognize they are role models watched by people all over the world," the former South Africa all-rounder added.
"Cricket is, after all, a non-contact sport and when players fail to recognize that fact and engage in needless nudges, the type of which we saw yesterday (Wednesday), then that is where we have to draw the line.
"James Anderson is not a player with a reputation for bad behaviour and, as he reflects on what happened yesterday and the fine he has incurred, I am sure he will do everything he can to ensure there is no repeat of this unfortunate incident.
"I concluded that Runako Morton was the victim of James Anderson's aggression rather than guilty of bad behaviour."
To complete a bad day for England, Anderson's team-mate Stuart Broad was reprimanded for wearing white 'skins' under his coloured one-day uniform, something which is banned under an ICC protocol.
"As for Stuart Broad's offence, the regulations regarding clothing are there in black and white and teams are reminded about them on a regular basis," Procter said.
"The potential for problems with players, especially bowlers, wearing visible white garments in a match involving a white ball is obvious and hopefully this sanction against Stuart will serve as a reminder to him not to wear such garments in the future."
Anderson does have the right of appeal against his level two offence. Such an appeal must be lodged in writing with the ICC's legal counsel within 24 hours of the decision being handed down.
But for Broad's infringement of the rules, a level one breach of the code, the match referee's decision is final and binding.