The campaign, officially announced at a press conference in the West Bank city of Ramallah on Monday, aims to peacefully express opposition to Israel's occupation.
"What we care about in this campaign is to send a message to the Israelis and to the whole world, regardless of how many get our message, that says we want the occupation to end," 23-year-old activist Dina Jaber said.
Activists are calling on people to write phrases including "Let's end the occupation" and "Free Palestine" on banknotes of the Israeli currency, the shekel, which is also used throughout the West Bank and Gaza.
But the plan was not welcomed by everyone in Palestinian society, with the Palestinian Banking Society warning in a statement that defaced banknotes could lose their value.
"With all appreciation for the good intentions of the organisers of this initiative, the society urges all citizens to understand the negative impact the act could have on the Palestinian economy," the institution said.
"We inform citizens that banks operating in Palestine are unable to accept any banknote with a slogan written on it because it will be unable to exchange those banknotes with Israeli banks."
Organisers of the campaign said the objections ought to be no obstacle, and urged those worried about their money losing value to simply write the slogans on stickers that could be removed from the banknotes if necessary.
Jaber said activists were convinced that the campaign could send a powerful message to Israelis and foreigners.
"We monitor Israeli media and we think that our message is beginning to be understood: We want to end the occupation in a peaceful manner."