A children's charity said it is referring an average of 90 calls a week to police and social services over concerns a young person has been sexually assaulted.
The NSPCC said the figures form part of a total of 4,677 referrals made UK-wide last year, up from 3,578 in 2015/16.
There were also a further 3,912 contacts where helpline staff gave advice about sexual abuse against young people.
NSPCC Scotland revealed 265 cases were passed on to authorities in 2016/17, up from 187 in the previous year.
Similarly, there were 167 occasions where charity staff gave advice after being contacted about sexual abuse involving young people.
The NSPCC said children will not always realise they are being sexually abused, while non-physical offending can occur through live-streaming.
John Cameron, head of helplines at the NSPCC, said: "It is deeply worrying that so many children are potentially being exposed to such a devastating experience, but at the same time it also suggests that as a society we are much more alert to the risks and much more willing to come forward and share our concerns.
"Sexual abuse can do huge damage to a child's life and left untreated will often haunt them long into adulthood.
"It is therefore vital that anyone who suspects a young person is in danger contacts the authorities or gets in touch with us through our dedicated helpline."
The charity has launched a Light Up Christmas for Children appeal to help vulnerable young people over the festive period. For more information, visit NSPCC.org.uk.