O'Hara was also fined £2,500 for biting an opponent.
The incident is alleged to have occurred in the 44th minute of the 1-1 draw on February 29.
O'Hara was alleged to have bitten the arm of Peterborough forward Sammie Szmodics.
The FA released a statement on Friday night, saying: "An independent Regulatory Commission has suspended Kieran O'Hara for six matches with immediate effect and fined him £2,500 for a breach of FA Rule E3.
"The Burton Albion goalkeeper denied that his behaviour during the 44th minute of an EFL League One fixture against Peterborough United on Saturday 29 February 2020 amounted to violent and/or improper conduct but the charge was subsequently found proven.
"The independent Regulatory Commission's written reasons will be published in due course."
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