Jacobsen, who teamed with Fuzzy Zoeller to win last years event with six skins worth $320,000, said he tweaked his left shoulder while hitting balls last week. He is now unable to make a full swing.
The 54-year-old Jacobsen says out of respect for the event, he did not want to participate if he was not as his best.
Crenshaw, a two-time Masters champion and 19-time PGA Tour winner, will make his first skins game appearance.
The 57-year-old Texan and Zoeller will face the teams of Jack Nicklaus-Tom Watson, Greg Norman-Jay Haas and Gary Player-Bernhard Langer in the $770,000 event that starts Saturday.