Zafar Rushdie said his father had sustained life-changing injuries, but was able to speak to his family.
Rushdie, 75, was left severely injured after being stabbed on stage at an event in New York state.
He has faced years of death threats for his novel The Satanic Verses, which some Muslims see as blasphemous.
The man charged over Friday's attack has pleaded not guilty to attempted murder.
"Following the attack on Friday, my father remains in critical condition in hospital receiving extensive ongoing medical treatment," Zafar Rushdie tweeted.