The Rugby Football Union (RFU) said the Harlequins player had accepted a charge of striking Sale flanker TJ Ioane with his shoulder last Saturday and would not be available until Feb. 20.
England's third match of the championship is against Scotland at Murrayfield on Feb. 24.
An independent disciplinary panel found that contact was made with Ioane's head and it handed Marler a mid-range penalty.
"The panel considered that the player's previous record was such that it required an additional period of suspension of one week," said panel chairman Philip Evans.
"However because of his plea, his conduct since the incident took place and other personal mitigation, the panel allowed some reduction."
The suspension is the 27-year-old's second of the season, the prop having been given a three-week ban last October for use of the elbow.
England centre Ben Te’o will also miss the start of the Six Nations after his club Worcester Warriors confirmed at a news conference on Tuesday that he would be out for another month with the ankle injury he sustained in October.
Defending champions England face Italy in their Six Nations opener on Feb. 4 before meeting Wales six days later.
(Reporting by Alan Baldwin, editing by Ken Ferris)
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