Pitching for the South Bend Silver Hawks, Allen almost threw a perfect game, retiring 27 of 28 batters and striking out nine along the way to a 2-0 victory over West Michigan in the Class A Midwest League.
Allen stands 6 foot, 4 inches and played for Arkansas State in college. This is his first season with the Arizona Diamondbacks.
It was the franchise's first no-hitter since 2002, according to milb.com.
Allen is 7-6 this season with a 4.67 ERA.