"Aggressive player, benevolent man - so easy to love," Anushka posted on her Instagram story, along with a news snippet of Virat's act.
Smith was constantly booed by Indian fans during the World Cup fixture between India and Australia at the Kennington Oval which the Indian team won by 36 runs.
Smith, who was the captain when the Australian ball-tampering controversy took place last year, was first booed, with chants of "cheater, cheater", making the rounds while he was fielding at third man during the Indian innings. All-rounder Hardik Pandya had just been dismissed, and the crowd tried to get under Smith's skin with the chants.
Indian skipper Virat Kohli, who was batting at the time, looked up towards that section of the stadium and gestured them not to do so. He instead made a "clap" gesture and pointed towards Smith. He also did the same when Smith walked past, with both players shaking hands.
Commenting on it in a post-match press conference, Kohli expressed sympathy for Smith and apologised on behalf of the Indian crowd.
"Just because there are so many Indian fans here, I just didn't want them to set a bad example, to be honest, because he didn't do anything to be booed, in my opinion," Kohli said.
Apart from Anushka, actor Ayushmann Khurrana was also impressed by Kohli's on-field gesture.
"A true icon. Well done captain," he tweeted.
( With inputs from IANS )