The 20-year-old Koval departed LSU after one season and was initially reported to have left the programme for "personal reasons" following Minaeva's arrival.
Koval later explained that Russia's ongoing invasion of Ukraine was the reason behind her decision to step away from the team.
"My father serves in the Ukrainian military and takes tremendous pride in defending his country against Russian aggression," Koval wrote in a statement shared on Instagram.
She said the war had a deeply personal impact on her family and those close to her, making it impossible for her to view the conflict as something distant.
"People close to me have been killed and wounded in Russian attacks, and places where I grew up and first began playing basketball have been destroyed by missile strikes," she wrote.
Koval said the timing of Minaeva's arrival and the emotional impact of the war led her to reconsider whether LSU was still the right environment for her.
"This decision has not been easy," she said. "While I understand and respect that roster decisions are a part of college basketball, I have to remain true to myself, my values and my country."
Koval had been expected to become LSU's starting centre this season. She has two years of collegiate eligibility remaining.
However, the NCAA transfer portal has already closed, leaving Koval uncertain about her next move. She said she hopes the National Collegiate Athletic Association will take her circumstances into account and allow her to transfer to another university for the upcoming season.
"I felt I had found a home at LSU," Koval said. "I am incredibly grateful for my teammates who became family, as well as my coaches, staff, professors and the entire LSU community."
Koval also expressed appreciation for the experiences she had during her time at the university, despite ultimately deciding that she could no longer remain with the programme.
"I will always cherish the relationships, experiences, and memories I made there," she said.
Her departure comes as Russia's invasion of Ukraine continues to affect athletes and sporting organisations around the world. The conflict has created difficult decisions for athletes with personal ties to both countries, particularly when Russian and Ukrainian competitors are placed in the same sporting environments.
For Koval, her family's direct involvement in the war ultimately made the decision to leave LSU one she felt she needed to make.
