The reimagined mixed doubles competition, a two-day event featuring 16 teams, began on Tuesday but the official draw and order of play no longer featured the Sinner-Siniakova entry.
Danielle Collins and Christian Harrison replaced the Sinner-Siniakova partnership in the draw and will play Belinda Bencic and Alexander Zverev in the first round.
Sinner, the reigning Australian Open, Wimbledon and US Open champion, looked uncomfortable in sweltering conditions on Monday at Cincinnati, where he retired after falling behind 5-0 in the first set.
The main singles draw at the US Open is scheduled to begin on Sunday.
