Kostyuk, 23, told reporters that the missile landed during a massive Russian bombardment of the Ukrainian capital over the weekend.
“[The] majority of Kyiv suffered from something like this this morning,” she said. “It was half of the night, it was happening throughout, like, four hours.
“[My family] feel okay. Obviously very scary, but, you know, it’s not the first very difficult night, not the last, so, you know, they are adapting.”
Kostyuk said that the start of Moscow’s invasion of Ukraine in 2022 was the hardest moment because of the “unknownness” of the situation, but admitted Russia’s bombardment had shaken her.
“Right now, I think it was just the closest that it has ever been to my house, and this what probably makes it the most emotional,” she said.
“There are better days, worse days, but yeah, this one was, I would say top three worst ones, for sure.”
Although Kostyuk said she felt “sick” upon hearing the news, she never considered pulling out of the tournament.
“Everyone is healthy, alive … So these things, you know, it’s difficult, but none of my close friends or people I know is injured or dead,” she said.
“I don’t want to think what I would do if something worse happened, but I knew that this is the day to go out and play, and it didn’t cross my mind today that I shouldn’t go out.
“There were obviously times in the match when I would go in back to thinking about it, because most of the morning I felt sick just for my thought that see if it was 100m closer, I probably wouldn’t have a mom and a sister today.”
Since the outbreak of the war, Kostyuk has not shaken hands with Russian players before or after her matches.
The Madrid Open winner said the tour had “forgotten” about Ukraine in recent years.
“I live it always, and I have also adapted to the fact that the tour forgot about it,” she said.
“I’m still trying to do things that I can do and to what I can to influence, and I use my platform, I use my speeches or, you know, whenever I have a moment to remind about it, to remind of the horror of, you know, everyday lives of people.
“People adapt, people forget, people move on. There is a lot of issues in the world, a lot of wars, and things that people want to support or people are thinking about.”
Kostyuk’s next opponent will be Katie Volynets after the American beat France’s Clara Burel in straight sets.