On Tuesday, Boyce voiced his concerns regarding recent incidents of players going to ground easily in an attempt to win penalties.
"I watched the latest Suarez incident (against Stoke last weekend) two or three times and to me it is nothing less than a form of cheating," said Britain's representative on FIFA. "It is becoming a little bit of a cancer within the game and I believe if it is clear to everyone that it is simulation then that person is trying to cheat and they should be severely punished for that."
The Uruguay FA (AUF) are angry Boyce chose to single out Suarez, claiming his comments "encourage and provoke hostility" towards the 25-year-old Liverpool striker.
As a result they have written to FIFA president Sepp Blatter to complain.
"The Uruguay Football Association has become aware of statements made by the vice-president of FIFA, Mr Jim Boyce," said the letter by the AUF, which they also posted on their website.
"These expressions, refer to the Uruguayan player Luis Suarez, calling his conduct an act of "cheating" and that such a situation is a "cancer" for football.
"We understand that this kind of comment, coming from a person who holds the position of vice-president of FIFA - with specific reference to a football player and linking their actions to a disease that is a scourge on humanity - are at odds with the principles world football governing.
"The Football Association find unacceptable the comments made by this person."
"The Code of Ethics of FIFA clearly states: 'Officials should be aware of the importance of their role and the obligations and responsibilities that entails'.
"Deliberately ignoring his position and role, Mr Boyce has referred specifically to a football player, encouraging and provoking hostility towards them, especially if one takes into account the environment in which these expressions were made."
In their letter the Uruguay FA also listed a number of points they wish to be addressed, including calling for Boyce's conduct to be investigated by the world governing body's ethics committee.
Suarez is currently on international duty with Uruguay, who play Argentina in a World Cup qualifier in Mendoza on Friday.
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