There is a section in part six of Anna Karenina where Anna reveals to Dolly that it is impossible for her to have more children.
Anna hasn't received a divorce, causing Vronsky to be concerned that any children they might have will legally belong to Alexey Alexandrovitch.
Anna reacts with this section:
“What children?” Anna said, not looking at Dolly, and half closing her eyes.
“Annie and those to come...”
“He need not trouble on that score; I shall have no more children.”
“How can you tell that you won't?”
“I shall not, because I don't wish it.” And, in spite of all her emotion, Anna smiled, as she caught the naïve expression of curiosity, wonder, and horror on Dolly's face.
“The doctor told me after my illness...”
“Impossible!” said Dolly, opening her eyes wide.
The quick research I did on this section indicates that some readers consider this to be Anna revealing that she uses birth control.
This takes place in the late nineteenth century, so condoms and diaphragms were available. But a diaphragm would have been difficult to use regularly without Vronsky's knowledge and a condom would have been impossible.
The other option Anna had was the most common form of birth control in Russia at that time, abortion. I think Anna is either revealing here that she has had at least one abortion and intends to have others or that she has had a hysterectomy.
Either of those revelations would explain Dolly's reaction, but the two possibilities would give Dolly very different views of Anna. The Christian church existed in Czarist Russia in a number of different forms. Dolly is not presented as a devout follower, but she could have been influenced by what were then the current views of the morality of abortion. If that was the case she might have been appalled at what Anna had done. But Anna does say “The doctor told me after my illness...”, so there is a good chance Anna is talking about an operation that has left her sterile. If so, Dolly is reacting to what has happened to Anna's womanhood, from a nineteenth century perspective. In this case she would have been filled with pity for Anna. When she leaves Anna's home, Dolly seems more appalled than consumed with pity, but either way her reaction is interesting.
Once again, Tolstoy touches on a topic that is very relevant to a modern reader, even though his novel was written and set in the eighteen hundreds.