The 18-year-old, who has also been capped by England at youth level and been billed 'the next Jack Wilshere' was found guilty of "using abusive and/or insulting words…including a reference to ethnic origin and/or colour and/or race."
The incident happened in a match against Norwich City last season and the complaint is believed to have been made by the match officials.
The FA brought in a new rule this summer that says any discriminatory abuse must be met with a minimum five-match ban, but because the incident happened last season, Jebb escaped with just a four-match ban and a fine of £1,800.
Arsenal have a 'zero tolerance' policy towards racism and could yet discipline Jebb further.
The club's official website praises the progress Jebb has made at the club.
"Creative midfielder Jack, like his namesake Wilshere, joined Arsenal’s academy a year early - and has reaped the rewards," they write.
"The technically-gifted central midfielder made his breakthrough into the Under-18s last season, playing seven times and scoring his first goal against Leicester with a fine free-kick.
"Attack-minded Jack is an industrious figure in the engine room and can be deadly from set-pieces.
"He is also an England youth international and has been capped at both Under-16 and Under-17 level."