Sindhu outclassed Japan's Nozomi Okuhara 21-19 21-10 in the semi-final to assure herself of at least a silver medal.
Bindra, India's lone Olympic individual gold medal winner, took to twitter to congratulate the Hyderabadi shuttler.
"What a player !! @Pvsindhu1 I'm waiting for you to join me in the club. You have no idea how lonely it's been !!!," Bindra tweeted.
Prime Minister Narendra Modi also extended his best wishes.
"Way to go Sindhu! Congratulations! You have made India proud!!! All the very best for the finals," the PM wrote on his official handle.
"Superb performance @PvSindhu1. You make India proud! Best of luck for the finals," read another tweet from Modi.
London Olympics bronze medallist shooter Gagan Narang also joined fellow shooter Bindra in congratulating Sindhu.
"Super #PVSindhu nails #Rio2016 medal. May grey turn to yellow for you super girl! #GoYellow @Pvsindhu1 @pullelagopicha1," Narang wrote.
Bollywood Superstar Amitabh Bachchan was not behind.
"T 2352 - Never ever underestimate power of female gender ! #PVSindhu you have destroyed so many 'naysayers' .. you are the PRIDE of INDIA !," the mega star wrote.
Chess wizard Viswanathan Anand said, "@Pvsindhu1. Congrats... Medal in #RioOlympics2016. @OGQ_India. Go India Go Woman in sports!"
Star boxer Vijender Singh had his own style of eulogizing Sindhu.
"Bhaiyo es chori ne bhe lath gaad diya proud of #PVSindhu and wish u all the best for finale hope u come up wth gold ????," the London Olympics bronze medallist wrote.