The organisation's social media accounts have been silent since Friday's inauguration.
The new rules ban staff from publishing social media posts, press releases or blog posts and stops them publicising publicly-funded research.
"A fresh look at public affairs and communications processes is common practice for any new Administration," a statement from the EPA's office of public affairs said.
However, scientists are viewing this as a gagging order on climate change information, and censorship of scientific facts.
Organisers of the Scientists March on Washington have stated they plan to stand up to the Trump Administration and organise marches across the country.
They wrote in a blog post: "Although this will start with a march, we hope to use this as a starting point to take a stand for science in politics. Slashing funding and restricting scientists from communicating their findings (from tax-funded research!) with the public is absurd and cannot be allowed to stand as policy.
Thanks for all your support.
Please consider donating to the .@NatlParkService and help it keep up its great work. https://t.co/3wzhjrnN4B
— AltUSNatParkService (@AltNatParkSer) 25 January 2017
"This is a non-partisan issue that reaches far beyond people in the STEM fields and should concern anyone who believes in empirical research and science. There are certain things that we accept as facts with no alternatives. The Earth is becoming warmer due to human action.
"The diversity of life arose by evolution. Politicians who devalue expertise risk making decisions that do not reflect reality and must be held accountable. An American government that ignores science to pursue ideological agendas endangers the world."
Government employees appear to have been fighting back on Twitter, with the Badlands National Park tweeting then deleting climate change facts.
"Today, the amount of carbon dioxide in the atmosphere is higher than at any time in the last 650,000 years," one tweet said.
There is now also an unofficial National Parks staff Twitter account, which claims to be manned by Government staff.
They tweeted: "Can't wait for President Trump to call us FAKE NEWS. You can take our official twitter, but you'll never take our free time!"
The account has been tweeting climate change facts.
Donald Trump has long appeared to be a climate change sceptic.
In 2012, he tweeted: "The concept of global warming was created by and for the Chinese in order to make U.S. manufacturing non-competitive."
In 2014, he tweeted: "NBC News just called it the great freeze — coldest weather in years. Is our country still spending money on the GLOBAL WARMING HOAX?"
And in 2015, at a rally in Hilton Head, he said: "Obama's talking about all of this with the global warming and … a lot of it's a hoax. It's a hoax. I mean, it's a money-making industry, okay? It's a hoax, a lot of it."
The White House deleted the climate change policies on its website on the day of the inauguration.