The Minnesota Twins originally selected Neshek in the 45th round (1,337th overall) of the 1999 MLB draft, but he did not sign and went on to Butler. The Twins again later drafted him in the sixth round (182nd overall) of the 2002 MLB draft. He signed with the Twins that year for a $132,500 signing bonus, and was assigned to the Twins' rookie farm team. He then spent four years in the minor leagues. During the 2005 season, he led all minor league Twins players in saves. In 2006, Neshek was 6–2 with 14 saves and a 1.95 ERA in 33 relief appearances for the Triple-A Rochester Red Wings. He was International League Pitcher of the Week on July 2, mid-season All Star, post-season All Star, Baseball America Triple-A All Star, and MiLB.com Triple-A Relief Pitcher of the Year. He has pitched innings in 302 career minor league games with 464 strikeouts, a 31–19 record and a 2.58 ERA.
