It said the increase is particularly noticeable in Makira Province which was closest to the epicentre of last month's 7.8 magnitude quake.
The head of UNICEF Solomon Islands Yun Jong Kang said a health awareness campaign would be broadcast on national radio and health messages sent to mobile phones to try and address the increase in illnesses.
He said health workers, volunteers and parents would also be using health and hygiene brochures and flip charts to encourage better hygiene in homes and around the community.
Mr Kang said his office is also continuing its support to local disaster authorities with education, water and hygiene supplies.
About 10,000 people were believed to have been affected by the quake across three provinces.
An 11-year-old girl on Guadalcanal who was crushed when a building collapsed on her is understood to be the only fatality of the quakes.
UNICEF is also supplying soaps, water containers and buckets to encourage families to practice constant handwashing and ease the burden of carrying and storing water.
Tents and tarpaulins from UNICEF would also be set up alongside affected schools ahead of the start of the academic year later this month to ensure children continue schooling while the repair work on schools take place.
The supplies will be distributed by Solomon Islands Red Cross health and hygiene promotion volunteers and in close collaboration with Makira Provincial Emergency Operation Centre (PEOC).
Photo:UNICEF / Tahu (Supplies including 3,000 pieces of hand washing soaps, 5,000 water containers, and 12 tents and tarpaulins for schools have been provided by UNICEF following a 7.8 magnitude earthquake in December 2016).