The former Cambridge United boss, appointed on October 5, says he could not fully commit to the club so felt it best he step aside.
Moors are bottom of the Vanarama National League following Saturday's 4-0 defeat at home to AFC Fylde.
A club statement said: "Solihull Moors are disappointed that Richard’s short time in charge has ended so soon and will commence the search for a replacement immediately.”
Richard Money told the club's website the reasons behind his exit.
"There are so many people at this club who have worked so hard to get it to the level it is playing at right now and it deserves to stay there," he said.
"To do so it needs someone who can fully commit to the clubs future and unfortunately I am unable to do that right now. I wish everyone, board, players and supporters every success and thank them for their help, kindness and understanding."