Anderson was found guilty of a Level 2 offence by Emirates Elite Panel ICC Match Referee Mike Procter in a hearing after play concluded in Birmingham on Wednesday.
The player was found to have breached clause 2.4 of the ICC Code of Conduct which relates to ''inappropriate and deliberate physical contact between players in the course of play.'' Anderson was found guilty of twice nudging against batsman Runako Morton during the West Indies' player's brief stay at the crease.
Then, after Morton was dismissed, Anderson was found to have run towards the departing player to start a further confrontation, this time a verbal one.
Explaining his decision, Proctor said: ''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.
''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, then that is where we have to draw the line,'' he added.
Procter found Morton not guilty of a Level 2 offence, clause 2.8 of the Code which relates to offensive language or gestures.
However, Anderson's seam bowling colleague Stuart Broad was found to have breached clause 1.1 of the Code, which concerns the ICC Logo Policy.
Broad wore a visible white garment under his playing shirt on Wednesday, something not permitted under clothing regulations.
Level 2 breaches of the ICC Code of Conduct carry a minimum penalty of a fine of 50 per cent of a player's match fee up to a fine of all that fee and/or a one Test match or two ODI ban.