The network issued the warning after Prime Minister Theresa May called a snap general election for Thursday, 8 June.
RSN chief executive Graham Biggs said: "The Prime Minister called this general election to strengthen the UK's hand during Brexit negotiations."
"Given the amount of support it receives from Brussels, the rural sector will be among those most affected by the UK's decision to leave the European Union.
"In seeking to be elected or re-elected to parliament, it is vital that politicians remember the needs of our rural communities – and we will be fighting to ensure the rural voice is heard."
Other leaders representing rural communities have also spoken out ahead of the election.
They include Helen Woolley, director general of the Country, Land and Business Association.
She said: "We welcome the opportunity to get out and engage with candidates about the future of the countryside and ensure the rural voice is heard.
"The CLA will work throughout the campaign to ensure MPs understand that the future of the rural economy must be a national priority through Brexit and beyond."
National Farmers' Union president Meurig Raymond said agriculture was arguably the sector that would be most impacted by Brexit.
NFU members would want to understand how each of the political parties planned to support profitable, productive and progressive agriculture and horticulture in the future, he said.
"The right post-Brexit trade deal is absolutely critical but equally well so is a new wider policy framework that better delivers for farming and the nation.
"Throughout the next seven weeks the NFU will ensure that all parties fully understand and engage with the food and farming community on the issues facing the sector both now and post-Brexit.
British farms produced the raw ingredients for the UK food and drink manufacturing sector which was worth £108bn and the public wanted to buy British food, said Mr Raymond.
"For that to happen it is vital that candidates recognise the enormous contribution that agriculture makes, said Mr Raymond.
For every £1 invested in agriculture, the NFU says farming delivers £7.40 back in returns to the national economy.