Josh Clayton, 23, from Taunton, has been missing since Sunday with teams of coastguards, police with dogs and a helicopter involved in the search.
Police urged "untrained and unequipped" searchers to be mindful of their own safety to avoid additional incidents.
Mr Clayton's disappearance has been described as "out of character".
His sister posted on social media that she was "overwhelmed" by the support.
Dani Clayton  posted on the Isles of Scilly Police Facebook site: "Thank you so much for all you are doing to help find my baby bro - Im positive he will be found soon. You are all doing an amazing job and i am overwhelmed by all the support from everybody. I cant thank everyone enough xx."
On the social media page, the force said the team had received offers of support from volunteers which was a "very human and compassionate response".
However, it said the "co-ordination and management of untrained, unequipped searchers is resource intensive" and does not provide the level of assurance needed to make sure they did not miss anything.
It said: "Using untrained volunteers at this stage risks distracting efforts from the task in hand.
"We ask that if people do make efforts to find him they are to be very mindful of their own safety so as to avoid us managing more than one incident."
Police confirmed the search for Mr Clayton, who has worked for the Tresco Estate for several seasons, will continue on Wednesday.
Untrained teams of volunteers searching for a missing man on the Isles of Scilly could risk distracting officers from the operation, police have said.