The FDNY said the tree fell near Central Park West and West 62nd Street at about 10:01 a.m.
PHOTOS: Fallen tree in Central Park injures 4
When first responders arrived at the scene six minutes later, they found the 29-year-old woman trapped under the tree. She had been struck in the head.
Minutes later, with the help of good Samaritans, the woman was pulled out from under the tree. She was taken to the hospital in critical condition.
There were three kids with her -- two in a stroller and one on a bjorn. The children were all taken to the hospital and are listed in serious condition, but emergency workers said they are expected to survive.
An eyewitness said the woman lost consciousness for a few minutes and then regained consciousness. The children were crying, but appeared to be OK.
"Crews have mobilized immediately to clear the tree and investigate the incident," the NYC parks department said in a statement.
The tree is maintained by the Central Park Conservancy.