White will miss Saturday's Guinness Premiership clash against Newcastle at Welford Road as a result.
The 34-year-old faces a disciplinary hearing in Dublin next Wednesday after being cited for allegedly punching an opponent during Leicester's Heineken Cup victory over Leinster last weekend.
But Tigers officials hit White with a seven-day ban following an internal hearing on Friday.
"Julian immediately accepted his guilt of the offence and has said he is very sorry for his loss of control," said Leicester in a statement.
"He knows that he has let down his team-mates and the supporters.
"He has apologised in respect of the incident and has been banned for seven days.
"He will miss the Guinness Premiership match against Newcastle this weekend."
White must now await the decision of an independent disciplinary committee next week.