Speaking after the Hammers' 2-1 FA Cup defeat to Stoke City on March 13, Grant suggested that the match official had been influenced in his decisions by the home crowd.
Grant's ban will commence with immediate effect and means he will miss Premier League clashes at Bolton this weekend and at home to Aston Villa the following week.
The Israeli made the comments after seeing his side crash out of the FA Cup at the quarter-final stage and claimed that his side should have been awarded a second-half penalty.
Grant hit out at referee Jones' handling of the second half, which began with Stoke being awarded a penalty just 13 seconds after the restart.
Matthew Etherington missed the spot-kick but Grant intimated he felt that Jones had been swayed by the home fans after Frederic Piquionne appeared to handle in the lead-up to the Hammers' opener in the first half.
"I think maybe this is the reason the referee started the second half very strange,'' Grant said of Stoke's penalty award. "Until they scored (the second) goal he gave fouls, a penalty, everything for them.
"It was a penalty for us at the end which he didn't give. What happened with (James) Tomkins was more bushido (the Japanese code of conduct for samurai warriors). Maybe he felt a little bit guilty. I think it was the effect of the first goal for us.''
Grant was charged with improper conduct for the comments on the same day that Manchester United manager Sir Alex Ferguson was given a five-match touchline ban and a £30,000 fine for his verbal attack on referee Martin Atkinson at Chelsea in February.
Speaking almost three weeks ago, Grant argued that fellow managers will stop giving honest answers if they continue to be reprimanded by governing bodies and echoed Ferguson's comments that "football is the only industry you can't tell the truth in''.
"I don't have much to say,'' said Grant. "I can say only that after the game in the interview I did not speak about the referee. Then one of the journalists asked me about the referee - ask him why he asked me - and I gave an honest opinion.
"I didn't put a question mark on the integrity of the referee or anything because I spoke with the referee, I shook his hand after the game. And again I gave an honest answer. If it is against the rules, I don't know.''
He added: "One thing for sure is I don't think the managers will give an honest opinion about [football decisions if this continues]. I am sure about this.''