"Today I have announced to the prime minister that I resign from the post as environment and food minister," Eva Kjer Hansen said in a statement, saying she did not want to "stand in the way" of the government.
The Conservative People's Party, which has just six seats in parliament but whose support is crucial to Rasmussen's minority government, on Wednesday threatened to withdraw its backing if the premier did not sack Kjer Hansen.
The party said it had lost confidence in the minister in a row over agricultural reforms.
But Rasmussen said he was not prepared to sack her, leaving the government's fate uncertain.
Rasmussen had held lengthy talks with the Conservatives in recent days in a bid to find a solution to the standoff, to no avail.
The Conservatives accuse Kjer Hansen of giving them wrong information about a proposed package of agricultural regulations, which they said could have serious consequences for the environment.
Hansen's critics specifically accuse her of giving in to the farm lobby on norms governing the use of fertilisers, leaving water supplies exposed to increased pollution from agricultural runoff.
In a statement on Saturday, Rasmussen said he had accepted Kjer Hansen's resignation "with great regret" and that he would appoint her successor "after the weekend".
Political analysts saw her decision to leave the government as a victory for Conservative leader Soren Pape Poulsen.
"Poulsen has won this arm wrestling against Lokke," TV2 News political commentator Anders Langballe said.