Alex W. Widmer, a prominent Swiss private banker, died Wednesday of what police are treating as a possible suicide, according to people familiar with the situation.

Overseeing the private bank at Julius Baer Holding AG, Mr. Widmer turned the Zurich firm into a leading bank for wealthy clients by poaching bankers from larger Swiss rivals UBS AG and Credit Suisse Group. He also expanded in Europe and the Middle East. The 52-year-old Mr. Widmer was a widowed father of three.