The letter read how Bachchan has always admired his work for his "presence and versatility" and his performance has been "exceptional".
Pannu, who has previously shared screen space with Bachchan in "Pink", shared her photo - sprawled on the floor with the letter in her arms and the flowers by her side.
"Finally! THIS LETTER! A milestone achieved!" the actor, who is set to reunite with Bachchan in "Badla", tweeted.
The love triangle also stars Abhishek Bachchan.
In the past, actors such as Rajkummar Rao, Deepika Padukone, Ranveer Singh, Ayushmann Khurrana, Sushant Singh Rajput, Kangana Ranaut and Randeep Hooda have received letters from Bachchan.