Mclean was sent off for a dangerous tackle in England's 29-15 win over Italy at Twickenham Stoop on Saturday.
England have won all three matches in the competition so far, but 2014 World Cup-winner Mclean will now miss the clashes against Scotland and Ireland.
Fly-half Mclean pleaded guilty to the offence which helped the disciplinary panel cut an initial six-week sanction in half.
"The England player, Katy Mclean, appeared today before an independent disciplinary committee, having been red-carded by the referee for dangerously tackling an opposition player during the Women's Six Nations match between England and Italy at Twickenham Stoop on Saturday, February 25," read a Six Nations statement.
"Ms Mclean accepted that she had committed an act of foul play which was worthy of a red card.
"The disciplinary committee, chaired by Roger Morris (Wales), alongside Jennifer Donovan (Ireland) and Julien Berenger (France), having reviewed the footage of the incident and all other evidence, as well as hearing submissions from the player and her representatives, categorised the offending as mid-range, which carries a six week entry point in World Rugby's sanction table.
"The committee further determined that there were no aggravating factors and the player had met all mitigating factors permitted, and therefore decided to reduce the entry point by three weeks.
"The player is therefore suspended from playing rugby for a total of three weeks.
"Taking into consideration that the player has no scheduled matches on the weekend of March 4/5, the player is suspended until midnight on Sunday, March 26.
"The player is therefore eligible to play again on Monday, March 27 and has the right of appeal."
