Neither player will travel to Saturday's opener against Navy in Dublin, Ireland.
"Our players are aware of the standards I set for our program and that failure to meet my expectations will result in consequences," coach Brian Kelly said in a statement. "Justin and Cierre violated our team rules so I've suspended them for the first two games of the season."
Wood, a senior, rushed for 1,102 yards and nine touchdowns last season. Theo Riddick, who has played both running back and wide receiver, likely will replace Wood as the Irish's No. 1 running back during the first two games.
Utupo, a junior, has seen mostly special teams action for the Irish during his career.
The players also will miss the Sept. 8 home game against Purdue.
The Irish also have lost starting cornerback Lo Wood for the season with a ruptured Achilles tendon. He underwent surgery on Wednesday.
Information from The Associated Press was used in this report.