"I guess Melania's Be Best campaign hasn't quite started to kick in," Kimmel joked.
SNL came out swinging this weekend with a cold open about Eric Trump receiving an unexpected visit from Robert Mueller, portrayed by Robert DeNiro.
He was one of at least eight people at a controversial June 2016 Trump Tower meeting.
"There is, and there are, people at the highest levels of government that don't want to let America be America," Trump Jr. said.
This will be the first Trump Organization project not to bear the president's name.
U.S. investigators are probing whether there was collusion between the Kremlin and Trump's Republican presidential campaign.
Kaveladze was once involved in a congressional money-laundering investigation.