The Friends and The Morning Show star said in an InStyle magazine interview published this week that there was still a "large group of people who are anti-vaxxers or just don't listen to the facts".
She added that she had, unfortunately, "lost a few people" from her weekly routine who would not disclose if they had been vaccinated.
She was challenged by some followers on Instagram, including Robyn Law, author of the weight-loss book The Body Plan, who asked why Aniston was worried about being around unvaccinated people when she has been vaccinated.
Aniston responded on her account.
"Because if you have the variant, you are still able to give it to me. I may get slightly sick but I will not be admitted to a hospital and or die. But I can give it to someone else who does not have the vaccine and whose health is compromised (or has a previous existing condition) - and therefore I would put their lives at risk," wrote Aniston.
"That is why I worry. We have to care about more than just ourselves here," she added.
Aniston, who has 37.7 million followers on Instagram, rose to fame as Rachel Green in US television sitcom Friends from 1994 to 2004. It followed a group of six New Yorkers in their 20s and 30s.