Moniwa was born in Atsugi on September 8, 1981. He joined J1 League club Bellmare Hiratsuka (later "Shonan Bellmare") from youth team in 1999. Although he played many matches as center back from first season, the club finished at the bottom place and was relegated to J2 League. He became a regular player from summer 2001. In 2002, he moved to J1 club FC Tokyo. He played many matches as center back with Jean until 2006. The club won the champions in 2004 J.League Cup which is first major title in the club history. However his opportunity to play decreased for injuries from 2007 and he could only 9 matches in 2009 season. In 2010, he moved to Cerezo Osaka. He played many matches as regular center back until 2012. However he lost his opportunity to play for injury from July. In 2014, Moniwa moved to Thailand and signed with Bangkok Glass. In 2015, Moniwa returned to Japan and re-joined Cerezo Osaka which was relegated to J2 from 2015 season. Cerezo was at the 4th place in J2 for 2 years in a row and was promoted to J1 end of 2016 season. In 2017, Cerezo finished at 3rd place in J1 League and won the champions in J.League Cup and Emperor's Cup. However he could hardly play in the match in 2017 and he could not play at all in the match in 2018. In 2019, Moniwa joined Japan Football League club Maruyasu Okazaki.