The former Serbia international was taken off in the fixture at Old Trafford following a collision with goalkeeper David de Gea.
He was taken to hospital after the match, but the club confirmed on Monday that their captain has now returned home.
"Nemanja Vidic was released from hospital on Sunday night after suffering concussion during the Barclays Premier League victory over Arsenal," the statement read.
United refused to confirm whether Vidic would be available for their next Premier League clash, a visit to Cardiff City on November 24.
Vidic will likely use the international break as a period of recovery, having retired from national duty - last featuring for his country in 2011.
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