The 12-day event, which has been drawing criticism for excessive length, was unable to stage the matches due to weather interruptions that have repeatedly plagued the tournament, which lasts for nearly as long as a Grand Slam.
The planned Monday matches between Spain's Rafael Jodar and Frenchman Arthur Fils and the clash between Italy's Luciano Darderi and American Brandon Nakashima were both rescheduled for Tuesday.
Defending champion Ben Shelton, the fifth seed from the United States, will face Czech Jakub Mensik and Spain's Daniel Merida will play American Learner Tien on Tuesday in the other quarter-finals.
The oddly scheduled Masters is not due to wrap up until Thursday's final, overlapping with the start of the Cincinnati Masters, the last major event before the US Open.
