Tutungi suffered serious neck and back injuries following a collision in the South Barwon and St Joseph's GFL game on the weekend.
Tutungi was airlifted to hospital where he remains.
His family released a statement on Sunday.
“The real damage is to the spinal cord and its functions, which control his body movements,” a statement released by parents Tully and Carol, and fiance Bridget said.
“He is in ICU (Intensive Care Unit) and as his health progresses we will know more over the next week about how his body will recover.
“Casey is a physically and mentally-strong person, but needs all the love and support you can give him in the future.
“We thank you for your heartfelt compassion; we appreciate it and need it at times like this.”
Geelong's players and coaches have used Twitter to express their sympathy.
Thoughts and prayers go out to casey tutungi #spirit
— Allen Christensen (@achristensen_28) June 22, 2013
Sending best wishes to Casey Tutungi from everyone at the Cats!
— Joel Selwood (@joelselwood14) June 22, 2013
Thoughts with Casey Tutungi. Praying for a good outcome for the little champion #spirit
— Dale Amos (@dale_amos) June 22, 2013