The abusive comments were largely made on the last Instagram post the Dutch defender had shared - on 14 February, wishing his wife a happy Valentine's Day.
Some of the messages contained wishes of harm on Pieters' wife and unborn child.
Pieters was in the thick of the action at Turf Moore after his introduction from the bench in the second half with the game at 1-1.
Arsenal thought they had a penalty when the ball struck Pieters' outstretched arm in the box, but no spot-kick was given despite a VAR review.
Shortly after, Pieters blocked a Nicolas Pepe shot with a goalline clearance and was shown a red card as the referee pointed to the penalty spot. But as replays showed the ball came off Pieters' shoulder, referee Andre Marriner reversed both of those decisions.
Regarding the abuse the 32-year-old full-back received post-match, Burnley released a statement on Twitter.
"We are aware of online abuse directed at Erik Pieters following yesterday's game," the club said.
"We are in contact with all relevant parties and offering our support to Erik and his family."
Players being attacked on social media - many of them black players receiving racist abuse - has been a growing concern in football.
There have been calls for social media companies to take greater responsibility for what is posted on their platforms, as well for the individuals involved in these hate crimes to be identified and held responsible for their comments.
Featured image credit: PA Images/BT Sport
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