Alongside the photo, the 38-year-old boxer wrote, "#family #klitschko #newyear."
Nashville actress Hayden, 25, looks radiant in the picture, just one month after giving birth to her first child. The engaged couple, who have been dating for five years, welcomed their daughter on 9 December.
"She's really so sweet," Hayden told People shortly afterwards. "I'm sure that's the way it's meant to be, because when they are putting you through the ringer you’re like, 'You are lucky you're so cute!'"
The star added, "You're suddenly looking at this little thing, like, 'Oh, that was you in my belly this whole time.'"
Hayden Panettiere and Wladimir Klitschko welcomed Kaya on 9 December
Parenthood has been a magical experience for both Hayden and Wladimir, who has "always wanted to be a dad".
"I think at some point he might gave started thinking he wasn't ever going to be (a father)," Hayden told the publication. "And then he was. He is just so over the moon."
Wladimir himself recently spoke of his connection with his daughter. "You don't know what love is until you have your first baby, then you know what love is," he told E! News.