"She does not want her day associated with them," a source told Us of the "Friends" sitcom and "Horrible Bosses" film star, who divorced Pitt in 2005.
Pitt and Jolie plan to get married in late spring or early summer.
Aniston, 44, first thought about moving her date up and getting married first, the source told the celebrity and entertainment magazine, but Theroux, 41, changed her mind.
"Justin got weirded out by all the rushing," the source said.
Aniston has put her wedding plans on hold, the source said. "Nothing has happened on that front in a month."
Aniston filed for divorce from Pitt, 49, in March 2005. It was finalized in October of that year.
There had been intense media speculation Pitt had been unfaithful to Aniston with "Mr. & Mrs. Smith" co-star Jolie, 37.
Aniston and Theroux, who co-starred in "Wanderlust," got engaged on the Theroux's 41st birthday last August, after 15 months of dating.