Defending champion Reid lost 6-3 6-2 to world number one and home favourite Shingo Kunieda, before Rio silver medallist Hewett was beaten 6-4 7-6 (5) by Holland’s Tom Egberink.
The British pair will battle each other for bronze on Saturday at Ariake Tennis Centre.
Before then they are scheduled to unite for Friday’s doubles final, seeking to upgrade the silver they won together in Brazil five years ago with a rematch against French reigning champions Stephane Houdet and Nicolas Peifer.
Fellow GB player Jordanne Whiley will also seek to salvage singles bronze following a 6-4 6-2 last-four defeat to Dutch top seed Diede De Groot in the women’s draw.
The 29-year-old will take on another player from the Netherlands, Aniek Van Koot, on Saturday with the final podium place at stake.