The United States and Israel launched air strikes on Iran over the weekend and the conflict has led to airspace closures and widespread flight cancellations across parts of the Gulf, disrupting a key transit hub for international sports.
Former world number one Medvedev, who won the Dubai Championships title via a walkover on Saturday, had been scheduled to play in the Eisenhower Cup, a one-night Tie Break Tens doubles event alongside fellow Russian Mirra Andreeva.
American Amanda Anisimova had been paired with Rublev for the popular event on the eve of the main draw of the Indian Wells tournament in the Southern California desert.
Seeded 11th, Medvedev's first singles match is scheduled for Friday. Rublev, the 17th seed, is also scheduled to play on Friday.