Number eight Leitch was dismissed for a high tackle on So'otala Fa'aso'o.
"The player accepted that foul play occurred and that the offending warranted a red card," World Rugby said in a statement on Thursday.
"The Committee noted that the offence carries a mandatory mid-range sanction (six matches), and having considered the mitigating factors reduced the sanction by the maximum mitigation of 50%."
Japan have three matches in the build-up to the World Cup, against Tonga on July 29, Fiji on August 5 and Italy on August 26.
World Rugby added that Leitch could still feature in the match against Italy by undergoing the World Rugby Coaching Intervention Programme, which would further reduce his suspension.
Japan are in Pool D with England, Argentina, Samoa and Chile at the World Cup, which runs from September 8 to October 28 in France.