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Schwarzenegger, 29, shared a photo of Pratt, 44, helping his son Jack, 6, chop wood.
"Happy Father's Day to my wonderful husband," Schwarzenegger wrote. "Watching you be such a hands-on and loving father was one of the many reasons I fell in love with you, and continue to each day. I love you."
Many of Schwarzenegger's friends and fans commented on the post, praising Pratt for his parenting skills.
"I can't with that miniature hatchet!" one person wrote.
"This is THE cutest thing," another added.
"So sweet!! I love this!! [heart][raised hands] Wishing you all a happy blessed marriage and can't wait until another baby Pratt!" another fan wrote.
Others decided to take the low road and criticize Schwarzenegger for sharing a photo of Pratt with Jack, whose mother is the Jurassic World star's ex-wife, Anna Faris. "I'll never understand why STEPmoms feel a need to throw BIOmoms under a bus," one person wrote.
Before sharing that photo, Schwarzenegger posted a slideshow of photos with her father, adding, "Happy Father's Day daddy! I love you so much (even when you feed Maverick from the table)!"
Pratt's own Father's Day post was a message to his late father, Daniel Pratt.
"Happy Father's Day to the strongest and funniest man I ever met. They don't make em like you anymore. Which in some ways is probably a good thing. Haha!!! Love you and miss you every day Pop," Pratt wrote.
Faris, to whom Pratt was married to from 2009 to 2018, shared a throwback photo with her father and brother. "Happy Father's Day!! I love you so much dad! And feel compelled by social media to let everyone know," she wrote on Instagram.
Pratt and Schwarzenegger married on June 8 at the San Ysidro Ranch resort in Montecito, California in front of Schwarzenegger's parents, Maria Shriver and Arnold. Her siblings were also there, as was Jack.
"Yesterday was the best day of our lives! We became husband and wife in front of God, our families and those we love. It was intimate, moving and emotional. We feel so blessed to begin this new chapter of our lives," Pratt shared in an Instagram post the day after the wedding.0comments
"We are so thankful to our families and our friends who stood with us and grateful to Mr. Giorgio Armani who created a once in a lifetime dress for Katherine to wear and for me, the perfect suit. This morning we feel nothing but blessed," he continued.
Photo credit: Getty Images