A large branch from a 50-year-old gum tree fell and landed on top of three students and a teacher on Friday afternoon at the small school in semi-rural north-western Sydney.

Eight year-old Bridget Wright, a horse lover and high-achieving year 4 student, was pinned beneath a limb of the towering tree and died after being rushed to Westmead Hospital.

A seven year-old boy escaped with minor scratches and his kindergarten-aged sister was admitted with serious injures.

Veteran year 2 teacher Warren Minton, 55, also suffered serious injuries although one of his two adult daughters said he was ''doing OK'' on Friday evening.

Just before 4pm, Bridget's father James took to Facebook to make a heart-breaking announcement.

''Just to let everyone know my darling princess has just passed away,'' he said. ''We ask that you have her in your thoughts and prayers. I love you my little Bridget.''

A woman who lives opposite the school, who asked not to be named, was gardening when she heard the thud.

''There were branches and the little girl was in amongst it,'' she said. ''There was two ladies with her talking to her.''

As children wept in front of the school, police cordoned off the fallen branch and forensic investigators and arborists arrived.

Hawkesbury Local Area Command Inspector Bill Slatford said weather played no part in the tragic accident.

The Department of Education recently applied for a development application to have 35 trees removed from the back of the school yet they had not proposed removing any from the front, raising fears among parents that the tree was at risk of coming down.

''The tree from which the limb fell today is not located within this rear section of the school, nor was its removal proposed with the approved Development Application,'' said Hawkesbury Council general manager Peter Jackson.

The small school of just 200 students and nine teachers rallied around Bridget's parents Alaina and James and sister Abigail on Friday evening.

''We're all trying to deal with this, it's a small community,'' said school mother Mel Walsh.

A father, Shane Morgan, whose daughter was ''a little shaken from what she has seen'', said he was angry. ''That tree should have been knocked down years ago,'' he posted online.

However other parents said the school was well maintained.

A spokesman for the Department of Education said arborists were regularly employed to assess and report on the condition of trees ''at the request of the principal''.

The department would not comment on the specific tree that killed Bridget ''due to a potential investigation''.

Witnesses said the school had responded very well.

''I can't praise them enough,'' said one woman. ''There wasn't chaos. They were very good. They got all the little children away from it.''