Jesus scored and provided an assist before being sent off in Brazil's 3-1 win over Peru at the Maracana on July 7.
The Manchester City forward remonstrated with the referee after receiving a second yellow card before pushing the VAR monitor and crying in the tunnel.
CONMEBOL announced a two-month ban for Jesus on Wednesday, a statement saying "the player is suspended to play official and friendly matches with his national team in that period of time".
Jesus was also fined $30,000 and is set to miss friendlies against Colombia and Peru next month, but has seven days to appeal the sanctions.
Meanwhile, Copa hosts and champions Brazil were fined $15,000 and warned for the behaviour of their fans.
It has been a busy period post-Copa for CONMEBOL, with Argentina star Lionel Messi and Chile's Gary Medel also receiving bans and fines.