According to a tweet from Golf Channel Insider Tim Rosaforte, Kirk broke his right hand playing with one of his sons. Kirk, who won the Colonial in May, has not played since the U.S. Open.
Taking his place in the field at St. Andrews is Kevin Streelman, whose name was atop the alternate list as the next highest player in the Official World Golf Ranking, at No. 80.
The next spot, which could be vacated by the visa-challenged Tim Clark, would go to No. 81: Japan's Hiroshi Iwata.
Russell Knox worked his way into the field earlier this week after Rory McIlroy officially announced he will miss the Open as he rehabs a ruptured ligament in his ankle.