Launchbury, 25, tried to kick the ball away at the base of a ruck but instead connected with Fiji centre Asaeli Tikoirotuma's head in the 42nd minute of the 58-15 victory at Twickenham.
He accepted he had committed an act of foul play, missed by the officials, that would have warranted a red card.
The kick was deemed reckless rather than intentional by an independent panel, resulting in what would have been a suspension at the lower end of the scale of four weeks.
But this was reduced to two weeks due to mitigating factors, including the Wasps captain's admission of guilt, his previous clean disciplinary record and good conduct at the hearing.
Launchbury can play again from Dec. 5, two days after England wrap up their autumn schedule, though he can appeal.
(Writing by Ken Ferris; Editing by Pritha Sarkar)
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