The ban was imposed at a RFU disciplinary hearing, chaired by Judge Jeff Blackett, at London's Bloomsbury Holiday Inn Hotel.
The suspension runs from May 18 until June 14 and Back was also ordered to pay Â£250 costs.
Sir Clive Woodward had already left the Leicester flanker out of his team for the Lions' friendly game against Argentina at Cardiff's Millennium Stadium.
He will also miss the opening three Lions tour matches against Bay of Plenty on June 4, Taranaki on June 8 and the New Zealand Maori side on June 11 but will be free for the game against Wellington on June 15.
The incident occurred during the first half of Leicester's 39-14 defeat by Wasps in flanker Back's final match for his club before retiring as a player.
Back, who admitted striking an opponent at the hearing, escaped immediate punishment from referee Chris White for the punch which left Worsley requiring 13 stitches in his mouth but an independent citing officer decided he should face disciplinary action after studying video evidence of the incident.