Tamim scored 71 and 78 as Bangladesh won their first-ever Test against Australia by 20 runs on Wednesday to take a 1-0 lead in the two-match series.
According to the International Cricket Council, Tamim was charged by match officials after he objected to the regular changing of gloves by Australia's batsmen and engaged in a verbal exchange with the umpires Wednesday.
Shortly afterwards, he approached wicketkeeper-batsman Wade and gestured towards im to leave the field upon his dismissal by Shakib Al Hasan.
The prolific left-hander was also handed one demerit point for the two offences.
The second Test will be played in Chittagong from September 4-8.