The Bulldogs have decided against taking the case to the tribunal, meaning Smith will miss the post-bye games against GWS and Hawthorn.
Smith was reported immediately after a three-quarter time scuffle with Tuohy during Friday night's pulsating Geelong win at Marvel Stadium.
"I'm disappointed to be missing the next two matches, and regret that I won't be able to help my teammates on the field during that period," Smith said in a club statement.
"I understand what happened was outside of what's expected of AFL players. Unfortunately, I let my emotions get the better of me, which is out of character for me.
"I am determined to come back in a couple of weeks to continue giving 100 per cent for my teammates and the club."
Match review officer Michael Christian upheld the report as intentional, with medium impact and high contact.
Tuohy was also reported for 'other misconduct' on Smith.
The Geelong utility was offered a $1000 fine with an early guilty plea.
After the pair grabbed each other's jumpers, Tuohy walked away from the wrestle with a minor cut on his forehead.
Tuohy spoke to Smith post-game, saying there was "all love at the end".
"Emotions were getting the better of both of us," Tuohy told Fox Footy.
"I think I was pulling and dragging at him as much as he was me, so there's not much in it."
Smith, who has never been reported before, has become one of the Bulldogs' most important players since being drafted in 2018.
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