An Independent Regulatory Commission found the former Chelsea and Portsmouth boss guilty of improper conduct relating to comments made to the media in the aftermath of the Hammers' 2-1 FA Cup defeat to Stoke on March 13.
Guilty! Grant has been banned from the touchline for two games after derogatory comments made about Jones
Grant's ban will commence with immediate effect and means he will miss the vital Barclays 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 competition 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.
Heads, you lose: West Ham were dumped out of the FA Cup after losing to Stoke at the Britannia Stadium
'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'.
Down and out: Grant was found guilty after comments he made proceeding West Ham's defeat at Stoke
'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.'
West Ham confirmed they will make a statement on the punishment in due course.
West Ham 2 Man United 4: Rooney bags a hat-trick leaves title in sightInspirational West Ham skipper Parker is player of the year, says boss GrantStay up and the future's bright: Grant rallies Hammers for relegation dogfightWest Ham United FC news, features and opinion Explore more:People: Matthew Etherington, Alex Ferguson, Martin Atkinson Places: Chelsea