He body was found and retrieved from a building adjacent to Gaza's largest hospital, Al Shifa Hospital.
The IDF sent "heartfelt condolences" to her family and said it would "continue to support them".
Photos show the parents, friends and family of Noa, who was 19, crying on each other's shoulders as her coffin was carried by Israeli troops and covered in floral tributes in a funeral service.
Large photos of the teenager - one of her in a graduation mortarboard and gown - were placed on easels at a large funeral service attended by military personnel and loved ones at a cemetery in the central city of Modi'in-Maccabim-Re'ut.
The young soldier's mother and friends were seen wearing white t-shirts with a photo of Noa on the front.
Noa is one of two female hostages found dead in Gaza by Israeli troops this week, the IDF said.
The body of another hostage, 65-year-old Yehudit Weiss, were recovered on Thursday, the military said, adding that she was kidnapped from her home in southern Israel.
Four hostages taken in the initial Hamas attack have now been confirmed dead, while four others have been freed and one rescued.
The war, now in its sixth week, was triggered by Hamas' October 7 attack in southern Israel, in which the militants killed more than 1,200 people, mostly civilians, and captured some 240 men, women and children.
Families of the Israeli hostages and thousands of supporters marched towards Jerusalem on Friday, putting pressure on the government to secure the captives' release.
The procession had left Tel Aviv three days ago. They held up pictures of their loved ones, waved Israeli flags, and chanted "We won't give up, we demand the hostages' release!"
Meanwhile Israeli troops continue to search Al Shifa Hospital for Hamas militants after claiming the militant group had built tunnels underneath the hospital and were using Palestinians as human shields in the conflict.
Hamas has denied this.
A doctor at the Gaza Strip's Al Shifa hospital said on Friday that food and water were running out and that supplies provided by the Israeli military were "very, very minimal".
Doctor Ahmed El Mokhallalati told Reuters that Israeli forces were pressing on with searches of the hospital complex, but had "found nothing".