The 49th-ranked Vesely pulled out of the event a couple of hours before taking the court at Arthur Ashe Stadium. The left-handed Vesely hurt his arm in Winston-Salem (N.C.) last week and had to retire from his final match before the U.S. Open.
"Playing Novak you have to be 100-percent ready," Vesely said. "I'm very, very disappointed right now. I was looking forward to that match. It's something that me or any young player is excited to play on the biggest court in our tour - obviously playing against Novak, against the No. 1 in the world. I had nothing to lose. It's just a lot of fun."
Vesely beat Djokovic 6-4, 2-6, 6-4 on clay in Monte Carlo in April.
Djokovic, the 29-year-old Serbian and two-time Open winner, has struggled with his own arm and wrist injuries since the Rio Olympics.
On Monday night, Djokovic brushed aside those injuries to claim a four-set victory over Jerzy Janowicz. The men's top seed and defending champion received an arm massage after the fifth game.
A title at the U.S. Open would make Djokovic only the second player in the Open era to win three Slams in consecutive seasons. He would join Roger Federer.
Djokovic will play either Guido Pella or Mikhail Youzhny on Friday.