Smith, who made his Test debut a decade ago, says he was humbled to equal with Meninga and will now break that record against New Zealand in Coventry.
Darren Lockyer has the record for most games for the Kangaroos with 59.
Smith played 40 minutes in the 54-12 rout of the Bravehearts in Hull.
The Australia captain set up one try and led his team around the park with aplomb.
“We were actually on our team walk this morning and Mal grabbed me and let me know I was equlalling his record,” Smith joked after the Scotland win.
“It was funny I got 46 Test matches and 23 I captained, and that’s what Mal finished with. He said this will probably be your last game too, so hopefully I get another start!”
Smith said he has long looked up to his fellow Queenslander Meninga.
The hooker has been coached by the 56-year old for some several years at State of Origin level.
“Mal was a guy I looked up to as a young boy,” the Melbourne Storm star said.
“He was part of my dream to become an Australia representative.
“I’ve been luckily enough to be coached by Mal for a long time now, but obviously for the last 10 months at this level has been quite special.
“To be able to play the same amount of games as a Kangaroo legend, that’s quite humbling for myself.”