Bopanna and his Romanian partner Florin Mergea had earned 360 points with a semifinal place at Rome Masters.
A top-10 player has the luxury of choosing his partner for the doubles competition at the Games.
Leander Paes, who is gunning for his seventh Olympics and is playing at the Challenger level to earn points, was back in top-50 with a jump of four places.
The next best in the doubles was Purav Raja, who gained two places to be 104 while Saketh Myneni, who lost a few weeks due to a shoulder injury, dropped to 125th after losing nine spots.
But Ramkumar Ramanthan was at his career best rank of 199th, breaking into top-200 for the first time. He had the semifinals at the Samarkand Challenger last week.
Meanwhile, Sania Mirza continued to be world number one in women's doubles ranking after winning the title in Rome.