Aniston and Theroux announced over the weekend that they are planning to get married after Theroux proposed on his birthday on Friday.
Aniston's father, Days of Our Lives star John Aniston, was later asked about the engagement in an interview with Celebuzz.
"It's the first I've heard about it," he said. "It's a surprise to me."
However, a rep for the former Friends actress has now told Us Weekly that John Aniston knew about the engagement but was worried about telling the media.
"[He] thought he was being trapped on the phone so played dumb to be safe," the spokesperson said.
Aniston has previously praised Theroux, describing him as a "charming young man" and saying that he and Jennifer "make a wonderful couple".