Representatives for the pair have not commented on the baby news.
The arrival of the baby boy comes three months after Dunst confirmed the pregnancy in the Fall/Winter portrait series for Rodarte, the label co-founded by her best friends, sibling designers Laura and Kate Mulleavy.
In the look book, Dunst cradled her baby bump while wearing a selection of stunning looks. See the photos here.
Dunst, 36, and Plemons, 30, met while filming season 2 of the FX anthology series Fargo. They played a married couple, Peggy and Ed Blumquist. They became engaged in January 2017, with the two mainly staying out of the spotlight until news of their pregnancy broke in December 2017.
While neither star has spoken about the baby or even the pregnancy, the Bring It On alum did hint at wanting to have a baby back in June 2017. She told Marie Claire UK that the birth of her goddaughter made her think more about having children.
"It's time to have babies and chill," Dunst said.
"I put her to bed last night, and she woke up this morning and said to her mom, 'Where's Kiki?' I just love that love. That's what I want," she said.
Dunst and Plemons are reportedly set to wed this spring in an intimate and understated event.
"Courthouse, dinner party and DJ with friends and family," Dunst told In Style UK in 2016 of her ideal nuptials. "I'll treat it like it would be my fortieth birthday."
Rodarte designers Kate and Laura Mulleavy will be designing her gown.
"I can't imagine not doing it," Kate told Us Weekly at the Woodshock premiere in Los Angeles in September.
Although she told PEOPLE in June that she's "not in any rush" to tie the knot, the Hidden Figures star revealed to Kelly Ripa and Ryan Seacrest months later that she'd been using Pinterest to brainstorm ideas.
"It's really fun, and because we create it together from the beginning, it's a really nice thing to do together," she said. "It's going to be so personal and fun. We're having a really good time."