Amendments abolishing the unprecedented tax, imposed about a month ago, will come into effect after approval by parliament, where Environment Minister Jaanus Tamkivi will deliver a speech on June 2.
In early May, Estonian farmers received tax notices for methane emissions, which ruminants produce in large quantities mainly through eructation (belching), but also through flatulence, when they digest grass.
According to a Food and Agriculture Organization report, cattle account for 18% of total greenhouse gas emissions.
The tax would have charged large farms, which house more than 300 cows or 2,000 pigs, around $5,000 each.
The country's opposition party, the People's Union of Estonia, protested against the tax, which they said came as a huge surprise, as no other EU country has adopted such measures.
However, the environment minister told a news conference that the tax could be reinstated if approved by the EU, and stressed that methane is by far more potent greenhouse gas than carbon dioxide.
A single cow produces on average 350 liters of methane and 1,500 liters of carbon dioxide per day.