Amin Khajeh Khalili had 12 points for Iran and Abdelrahman Elsayed led Egypt with 15 points.
Iran is scheduled to meet Morocco on Tuesday.
The 2021 FIVB Volleyball Men's U-21 World Championship, contested by the men's national teams under the age of 21 of the members of the FIVB, is being held in Italy and Bulgaria from 23 September to 3 October 2021.
Iran is the competition’s defending champion.