Tour operators and guides have also been given instructions about the locations of the banned areas in a meeting on May 24, according to Phuket News.
So far, around 40 buoys have been set up to mark these out in the waters.
The proposal is that the local government will police the waters to ensure the bans are fully enforced.
In addition, notices will be posted in several languages to alert visitors of the ban.
DMCR regional chief Watcharin Na said: "We want operators and guides active in Phang Nga and the surrounding areas to understand the rules and procedures in conducting a tour to prevent further damages to our marine natural resources and the coastal area.
"They must practice environmentally friendly tourism."
According to Watcharin Na, there were at least 60 speedboats visiting the sites per day before the ban.
He said: "Tour groups spend at least three hours swimming, feeding fish and snorkelling in the water, which severely damages the marine ecosystem, especially on coral reefs."
Surveys of the coral in the area by Phuket Marine Biology Centre has shown that around 80 per cent of the reefs have suffered some damage, particularly via coral bleaching.
Further damage could be caused by tourists' direct interactions with the corals, including handling the wildlife in the water and breaking off parts of the reef to take home.
It's not clear at present whether the ban will be permanent.
Thailand has been stepping up on the protection of its islands recently.
Last week, it was reported that a ban has been issued for the island of Koh Tachai, off the west coast of Thailand.
Professor Carolyn Roberts, Professor of Environment, Gresham College, London, told MailOnline Travel: "This island (Koh Tachai) sits within a Marine Preservation Zone, where the Thai Government are making, in my view, a genuine attempt to preserve some of the rare and exotic marine species.
"The Andaman area is noted for coral reefs, turtles and rare crabs. Visitors cause damage in the sea by breaking off pieces of corals and disturbing the larger marine species.
"Inland, away from the beaches, they can inadvertently damage ecosystems by trampling, disturbing the wildlife and pulling down timber for beach fires.
"They also tend to leave litter, and obviously toilet facilities are limited and human waste is damaging to local flora. All in all, I would applaud efforts to allow the island time to recover."
The ban to Koh Tachai will be enforced from October 15 for an indefinite period to protect the corals from irreversible damage.
It's hoped that the ban will allow the corals to recover.
MailOnline Travel has contacted DMCR for comment.