The 32-year-old wing player signed with the Pacers on Sunday after he received a buyout from the Knicks, the team announced.
Matthews was sent to NY from the Mavericks in late January as part of the Kristaps Porzingis trade.
Oladipo went down with a season-ending quadriceps injury last month.
Pacers president of basketball operations Kevin Pritchard called Matthews a "solid professional" who will "fit in well" with Indiana.
Terms of the deal were not available.
Wesley Matthews wasn't a free agent for long.
Matthews spent the past three-and-a-half seasons with the Dallas Mavericks before being dealt to the Knicks as part of the Kristaps Porzingis trade on January 31.
He's a career 38.2 percent shooter from 3-point range.