 Minahan was elected as a Democrat to the Sixty-sixth Congress, serving in office from March 4, 1919 to March 3, 1921, but was an unsuccessful candidate for reelection in 1920 to the Sixty-seventh Congress.He was again elected to the Sixty-eighth Congress, serving from March 4, 1923 to March 3, 1925.He was unsuccessful candidate for reelection in 1924 to the Sixty-ninth Congress and for election in 1930 to the Seventy-second Congress.