The awards were attended by Hilton just hours before she was jailed for violating probation on an alcohol-related drink-driving conviction.
"I said some very hardcore jokes about her.... Paris, I am really sorry," Silverman said.
Hilton responded by saying she was "shocked... and pleasantly surprised".
She added: "[Silverman] was so genuine and so sweet and it really moved me. I felt emotional hearing it and I could tell she really did mean what she said when she was apologising.
"Thank you, I really, really appreciate you doing that."