A snag has hit the insider-trading investigation of investor Carl Icahn, golfer Phil Mickelson and sports bettor William "Billy" Walters: News of the probe derailed government efforts to secretly deploy wiretaps, which have been key components of many successful insider-trading cases.

Criminal and civil investigators are examining whether Mr. Icahn tipped Mr. Walters about his plans relating to stocks of several companies, including Clorox Co., according to people briefed on the probe. The investigation...