Paris also posted a photo of herself cradling 32-year-old Nicky's baby bump, saying she "can't wait to meet" her sister's new daughter.
"Makes me so happy to see my sister so happy, beautiful, & glowing. So excited for her starting her new family," Paris Hilton wrote in another Instagram post of the two siblings.
News Nicky Hilton was expecting broke early this year, in mid-January. The pregnancy occurred six months after the hotel heiress married British banker James Rothschild. They married in London's Kensington Palace.