He was selected by the Baltimore Colts as the first player in the 1955 NFL Draft. Shaw quickly became the starter, but in the early part of the 1956 season, he suffered a broken leg and was replaced by rookie backup Johnny Unitas. As Unitas embarked on his legendary career, Shaw lasted two more years in Baltimore as the backup before being traded to the New York Giants, where he played two seasons. Shaw played one season with the Minnesota Vikings, where he started the first game in franchise history but was replaced in the first half by rookie backup Fran Tarkenton who took over the starting job. He also played one season with the Denver Broncos of the American Football League before retiring from football in 1962.