The Football Association said in a statement on Friday that Gray had also been fined 25,000 pounds ($32,417) and warned about his future conduct.
The 25-year-old had requested a personal hearing but was found guilty of six aggravated breaches of FA rules regarding comments deemed to be "abusive and/or insulting and/or improper and/or bringing the game into disrepute".
The breaches also included a reference to "sexual orientation and/or gender and/or colour and/or race," the FA said.
Gray apologised immediately after his comments came to light, saying he was at a very different point in his life four years ago.
His Premier League team said on their website (www.burnleyfootballclub.com) that the club and the player accepted the decision.
"Gray himself regrets the posts and has pledged, in an apology, to continue to improve, both as a person and role model to others," the club said.
The suspension means Gray will miss Monday's league game against Watford plus matches against Arsenal, Southampton and Everton.
(Reporting by Toby Davis; Editing by Tony Jimenez)
