Ukraine's Svitolina, the world number six, married French player Monfils in July 2021, and they have a four-year-old daughter together.
"I need to find my way back to myself, and I cannot do that within our marriage," the 32-year-old Svitolina said in a social media post.
"It is the hardest truth I have ever had to face and the hardest thing I have ever had to tell the person I love."
Monfils, 40, retired from tennis earlier this month, despite having been expected to make farewell appearances in Lyon and at the Paris Masters later this month.
He had been given a wildcard for this week's ATP 250 tournament in Lyon, but organisers said he had withdrawn for personal reasons.