Monihon was born to James and Ann (Martin) Monaghan, Irish immigrants, in Oneida County, New York on November 6, 1837.

Monihon joined the California Gold Rush in 1854, traveling by sea via the Isthmus of Panama.

[4]: 447  After reaching San Francisco, California, he became involved in placer mining often around Howland Flat, Sierra County until 1861.

[5] He remained in central Arizona, where he worked in mining again for several years[6] and ran a livery stable in Prescott.

[10] In 1870, he was a signatory to the formation of the Salt River Valley Town Association, the first government of the area that became Phoenix.

[7] In May 1872, he built a barn and corral for the Starar Brothers, from which they ran the Phoenix Livery, Feed, and Sales Stables on the corner of Washington Street and First Avenue.

[3]: 239 [6][a] He was on the board of supervisors in 1874,[3]: 239  and was nominated to run in the first mayoral election as the Republican candidate after Phoenix was incorporated in 1881.

[15] He was victorious in his third run in May 1894, winning by a large majority of 388 to 234 and leading a Republican sweep of all positions in the city election.

[16] He failed to win the Republican nomination in 1895 to Pierce Evans[17] who lost the election to the Democratic candidate.

[5] Monihon had an extensive association with Masonry, being a member of the lodge, chapter, commandery, and Mystic Shrine.

[4]: 448  He was a member and commander of the Civil War veterans' fraternal organization, Grand Army of the Republic lodge and was a delegate to the 1889 "National Encampment" in Boston.