The budding bodybuilder — a spitting image of his father — was spotted on social media at the gym while Katherine and Pratt, 39, celebrated their nuptials.
Baena follows Katherine and Patrick Schwarzenegger on Instagram, but neither follows him back.
Katherine previously came under fire for excluding Baena from a National Siblings Day post on Instagram.
Baena is Arnold's son with former housekeeper Mildred Baena.
Joseph was born in 1997, but Arnold didn't inform then-wife Maria Shriver of his paternity until 2011.
Katherine and Pratt married on Saturday at San Ysidro Ranch in Montecito, Calif., after having a rehearsal at Rob Lowe's home on Friday.
Pratt reportedly met Katherine through Shriver, who he knew through church.
Pratt gushed on Instagram, "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. 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."
They announced their engagement in January after seven months together.
Fox News' Nicole Darrah contributed to this report.