"Her first reaction was, 'Seriously?'" a source close to Kardashian told PEOPLE. "She didn't respond well at first. It's like she and Kanye had gone on this whole journey to get pregnant for months, and now this happens to Kylie. She teared up. It definitely took a lot of time for her to process it."
Kardashian, who is currently expecting her and husband Kanye West's third child via surrogate, was stunned by the news.
"It came out of nowhere," the source said. "It was the last thing on their radar. Kylie is just 20 and hasn't been with [boyfriend Travis Scott] for very long. So no one saw this coming."
The source stressed that while Kardashian was shocked at first, she's still happy for her younger sister.
"Of course Kim is happy for Kylie," the insider said. "She's going to support Kylie 100 percent, no matter what. There's never been any question about that. But it's just a weird dynamic, after all that Kim did to intentionally have another child. It has taken a lot of time, energy and money for her to get pregnant, and now Kylie is having a baby around the same time."
Kardashian realizes that her baby and Kylie's will presumably grow up together and be very close.
"This is ultimately really great news, because it's a new life," the source said. "They realize that."
"The babies will be the same age, and will probably be very close," the source added. "Family is everything for the Kardashians, so they're going to focus on these new kids in the family. Everyone is genuinely happy."
While the family is happy for Jenner's big news, they are being cautiously optimistic about Scott, because the relationship is so new.
"They don't know him too well," the source said. "They just want to make sure that this isn't a Blac Chyna situation. Kylie is so young and everybody is afraid that she could get really hurt."
Blac Chyna and Rob Kardashian have a tumultuous relationship while they co-parent their daughter, Dream Kardashian.