Momoi was born in Ishigami Village (now Minamisoma), Fukushima Prefecture, Japan, on 5 February 1903.
After graduating from the Fukushima Normal School, he entered the Faculty of Agriculture at Tokyo Imperial University in 1924. He graduated from the university in 1927, and the same year he was appointed as a chemistry teacher at a high school in North Hamgyong Province (present-day North Korea).
In 1928, Momoi married his wife, Tamiko, with whom he had five (or six) children. He served as a principal of two schools in Fukushima and Saitama respectively. He had lived in Saitama Prefecture since mid-1950s.
As an elderly man, he liked reading, especially Chinese poetry, and also practiced calligraphy. He smoked until the age of 90. His wife died in 2001. In 2015, his eldest surviving son was 84, and the third son, the one who was taking care of him, was 66. He resided in Chūō-ku, Saitama City until 2003, when he was moved to a rehabilitation hospital in Tokyo City.
Momoi died from a chronic renal disease at a hospital in Tokyo City, Japan, on 5 July 2015, aged 112 years, 150 days.