Mourners watched a live video of the funeral service held in Bloomfield, Conn., which began at 11 a.m. CT.
About 30 people from Winnipeg also flew down to the U.S. to attend the service.
Ana was one of 20 students and six staff members killed at Sandy Hook Elementary School after a gunman opened fire on Dec. 14 before taking his own life.
Ana's older brother, Isaiah, was also in a classroom in the school that day, but he made it out unharmed.
After three years of living in Winnipeg the Marquez-Greene family moved to Connecticut last July.
Ana's father, Jimmy Greene, is a jazz musician who was a faculty member at the University of Manitoba's school of music.
Her mother, Nelba Marquez-Greene, had worked as a family therapist at the University of Winnipeg's Family Therapy Centre.
In an interview a few day prior to the funeral, Alys-Lynne West, who spent a lot of time with the family while they were in Winnipeg, described Ana as "a little fireball of energy and a cute beauty."
"[She was] so articulate, so smart, and loving and curious," she said.
Alys-Lynne West, who organized a vigil for Ana earlier this week, handed out purple ribbons to those who attended.
"Purple is Ana's favourite colour," she said, adding that people were asked to wear purple to honour the little girl.