Paes, who has won eight medals at the previous editions of Asian Games, has not competed in the prestigious quadrennial event since winning the men's doubles gold with Mahesh Bhupathi and mixed doubles gold with Sania Mirza at the 2006 Doha Games.
Rohan Bopanna and his French partner Edouard Roger-Vasselin beat the American team of Taylor Fritz and Frances Tiafoe 6-3, 6-1 in just 63 minutes.
Yuki will be replaced by World No.246 Prajnesh for the tie which will be held in Tianjin, China on April 6-7.
Yuki Bhambri will now face eighth-seed American Jack Sock, who had received a bye in the first round.
In a stunning performance, the 110th-ranked Yuki Bhambri dispatched the ninth seeded Frenchman 6-4, 6-4 in an hour and 19 minutes.
Yuki, seeded ninth in the qualifiers, prevailed 6-4 6-2 in the second and final qualifying round to make it to the season's first Master series event.
Yuki Bhambri struggled to rein in his unforced errors and played well only in patches as his third Australian Open appearance ended with a straight-set first-round defeat at the hands of a seasoned Marcos Baghdatis on Monday.
Bhambri, who was junior world number one, had won Australian Open boys singles title in 2009 and has played only at this Grand Slam in the main draw since turning Pro.
Bhambri, seeded 15th, overcame Canada's Bradely Schuner 1-6 6-3 6-4 in the opening round and will next take on Spain's Carlos Taberner.
Bhambri pressed the self-destruct button by squandering six break chances in the deciding set and crashed out of the tournament.
India were left to battle it out in the Asian zone yet again after Ramkumar Ramanathan's defeat in the must-win fourth rubber as Denis Shapovalov steered Canada back to the elite Davis Cup World Group
Ramkumar Ramanathan fetched the crucial win but Yuki Bhambri made the day memorable even in defeat as India and Canada shared the honours on day one of the Davis Cup World Group Play-off tie.
India's big hope Yuki Bhambri crashed out of the US Open men's singles qualifiers with a three-set defeat to Japanese Go Soeda while Prajnesh Gunneswaran also suffered a tame defeat.
Ramkumar Ramanathan made it to the main draw as a lucky loser after Gael Monfils withdrew due to illness.
Yuki Bhambri and Saketh Myneni, injured during the Uzbekistan tie, return to Davis Cup squad as veteran Leander Paes is dropped.
Bopanna being the highest-ranked doubles player in the country is automatic choice for the doubles rubber.
Yuki Bhambri had stunned Gael Monfils, the defending champion at Citi Open, earlier.
Bhambri, who had qualified for the main draw of the ATP 500 tournament, took one hour and 51 minutes to register the 6-3 4-6 7-5 upset win over the sixth-seeded Frenchman to enter the round of 16.