"She helps me with everything. In return, periodically, I open a jar of pickles. That's the trade," he continued.
"Her heart is pure and it belongs to me. My greatest treasure right next to my Ken Griffey Jr Upper Deck Rookie card. Which if you know, you know is saying a lot.
"It's her birthday in about 6 weeks. So if I don't get her anything, I'll tell her to look back on this post. Love you honey," the actor added.
Pratt and Schwarzenegger welcomed daughter Lyla Maria in August 2020. The actor already had son Jack with ex-wife and fellow actress Anna Faris.
Jack, who is now 9, and thriving, was born premature and has undergone numerous surgeries for several health issues in the first few years of his life.
While he is now doing well, he still faces some challenges, like a visual impairment and a non-life-threatening heart condition.
People thought thanking his wife for his "healthy daughter" was offensive to his son.
"I love Chris Pratt, but the 'healthy daughter' part made me wince," one person tweeted, referencing the post.
"Although he may not have meant it as an insult, it sort of came off that way. Imagine how that will make his son feel, if he ever reads it?"
"Chris Pratt has a kid with Anna Farris [sic] who suffered a cerebral haemorrhage during birth and now has slight physical disabilities because of it. But he made sure to write 'healthy daughter' here. Chris Pratt is a d*ck," another person tweeted.
The actor's post was described by many as "disturbing" and making them "cringe".
Pratt's ex-wife Anna Faris has been open about the couple's son's health issues in the past.
"When Jack was born two months early, it came as a huge shock. And suddenly, your world completely shifts," the "Mom" star said on her podcast, Unqualified, in 2018.
"Jack had a few surgeries. He had a few hernia surgeries, he's had a few eye surgeries, and he had a little heart issue as well."
Pratt and Faris divorced in 2018, when Jack was 6.
He married Schwarzenegger in 2019.