Spain international midfielder Fabregas was sent off in the first half of the Premier League encounter against West Bromwich Albion away from home.
The former Arsenal captain was shown a straight red card just before the half-hour mark for kicking the ball at Chris Brunt.
Chelsea striker Diego Costa and West Brom centre-back Gareth McAuley became embroiled in a tussle, and as Mike Jones tried to restore order, Fabregas kicked the ball at the group of players around the referee, hitting Brunt on the head.
It was 1-0 to the Baggies at The Hawthorns at that stage, and the hosts eventually scored two more goals to win the contest 3-0.
QPR midfielder Barton was following the game, and he posted the following message on Twitter after Fabregas’s sending-off:
Some accuracy for Cesc. Very strange incident and red card that. Not sure what he was looking to achieve...?— Joseph Barton (@Joey7Barton) May 18, 2015
The defeat does not affect Chelsea this season, as Jose Mourinho’s side have already won the Premier League title.
However, Fabregas’s dismissal could have a affect next season, with ESPN reporting that Fabregas could get a three-game ban for his dismissal against West Brom.