The suspension followed an Independent Regulatory Commission hearing.
Mings and Manchester United forward Zlatan Ibrahimovic were both charged after a clash in Saturday's 1-1 Premier League draw at Old Trafford.
Ibrahimovic accepted the charge and was handed a three match ban on Tuesday, ruling him out of United's FA Cup quarter-final at league leaders Chelsea on Monday.
Mings had landed on Ibrahimovic's head with his studs just before half time and the Swede caught the Bournemouth player in the face with his elbow soon afterwards.
The incidents were not seen by match officials but caught on video.
Bournemouth expressed their disappointment with the decision in a statement, highlighting the player's "excellent disciplinary record".
Mings has not been sent off in 75 matches as a professional, receiving only 13 yellow cards with the last coming in April 2015, the club said on their website (www.afcb.co.uk)
"We will study the detailed reasons of the commission once they become available but find it extraordinary that the charges can be described as ‘proven’ when there is absolutely no evidence to prove the incident was intentional," it said.
"It is our strongly held belief – backed up by our relationship with the player, and knowledge of his background and character – that it was an accidental collision.
"Tyrone twice apologised to Ibrahimovic during the match for the accidental collision and also reiterated that there was no intent straight after the final whistle in a series of television interviews."
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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