The mark is the all-time Major League Baseball record.
Judge finished the contest at 1-for-1 with three walks and two runs.
MLB.com's Bryan Hoch noted the previous strikeout record belonged to Montreal Expos pitcher Bill Stoneman:
Although he has made headlines recently for his whiffs, Judge is in the midst of an impressive season. He won the Home Run Derby and is likely on his way to the American League Rookie of the Year.
He entered Tuesday's contest slashing .282/.413/.593 with 37 home runs and 80 RBI and is a primary reason the Bronx Bombers hold the top American League wild-card spot.
However, he was hitting just .169 with 32 strikeouts in August before Tuesday, per ESPN.com. New York will need him to rediscover his form if it is going to challenge the AL's top teams in October.